# Information Diffusion between Users in Open Data Ecosystem: Modelling and Simulation Analysis

Authors: Junjie Tang; Hongxian Zhu; Jiaxin Guo
Journal: Mathematical Problems in Engineering
 (2022)

---

## Abstract

Exploring the information interaction between users can provide a new way to solve open data ecosystem (ODE) sustainable development. In this paper, an information diffusion model, ILSOC, is proposed to analyze the information spreading among users within the ODE, and we use this model to inspect the impact on the sustainability of the ODE. First, we establish an information diffusion model that considers the public swing mentality. As a result, the relevant parameter variables are defined, and their influence is evaluated. Finally, this article proposes countermeasures to solve the sustainability problem within ODEs from the perspectives of users. Results demonstrate that (1) simply increasing the probability of interaction between users cannot effectively improve the sustainability of the ODE. (2) Parameters, such as contact rate, conversation rate, silent rate, and reversal rate, have constant effects on the ODE. (3) To maintain this ecosystem stability, some incentives and punishments for users in the public event are necessary.


---

## Body

## 1. Introduction

An ODE impacts the gross domestic product (GDP) of India by $22 billion [1]. The ODE, as a dynamic system of data utilization that has changed from “one-way” to “cycle” [2], provides new ideas for using data to solve problems in areas such as governance [3], entrepreneurship [4], community improvement [5], and university innovation [6]. Enabling an ODE with the support of high-tech [7, 8] can not only improve data quality and accuracy but also reduce the time and process of data acquisition [9]. In addition, this also promotes regional economic development [10] and strengthens the collaboration between governments, enterprises, and individuals, enabling them to calmly respond to data challenges [11]. However, due to a variety of reasons, including the weak awareness of data utilization and supervision by the public, data mismatch between supply and demand, low user participation [12], and loose connections between communities and institutions, the operation of ODEs has been severely affected, and the sustainable development of ODEs has become an urgent conundrum to be solved [13].In 2020, 142 Chinese cities settled open government data platforms, involving 98,558 government datasets in 33 fields [14], but most of these datasets are rarely used. Regarding the usage of open data in Zhejiang Province, which is ranked first in the provincial comprehensive ranking in China, although Zhejiang Province has opened 18,348 public datasets and 90,919 data items, the open datasets, including department information and future company evaluation information, have only been downloaded ten times. Additionally, as the other public budget statement views or downloads are just over a hundred, the data utilization is far less than expected.The data utilization by broad masses is the engine of the ODE, and users' open data effectively can bring many benefits to social, political, and economic development [15]. Greater user enthusiasm and a stronger ability to use open data result in both a more positive perception of data use and a greater value being placed on data. Therefore, more high-value data will become openly accessible, forming a virtuous ecological cycle [16]. Conversely, once the users become less willing and enthusiastic about using open data, thus influencing the utilization and feedback in the ODE, the data can lose its ability to create value. As a consequence, there will no longer be open access to datasets, which causes substantial financial losses and produces a vicious cycle.It will not be possible to convey the true value of open data by only studying the concept of an ODE or its users without considering user interaction. Information diffusion in the ODE refers to the user interaction in the open data platform. This concept is essentially the same as the spread of information and disease because of the exchange, transmission, and communication formed through contacts. Thus, the SIR epidemic model can be used to simulate the spread of information in the ODE.Therefore, we build a model using information diffusion theory [17] and integrate user interaction as the key factor. Then, the classic mathematical software MATLAB (MathWorks, Natick, MA, US) is depicted to simulate information diffusion processing between users with the aim of promoting the sustainable development of the ODE. The main contributions of this paper can be summarized as follows:(i)
An information diffusion model called ILSOC (I: ignorant individuals, L: latent individuals, S1: open data initiatives (ODI) supporters who know about the open data policy, S2 : ODI supporters who do not know about the open data policy, O : ODI opponents, and C: calm states) is proposed to explore the interaction between users of the open data ecosystem. Although it is common to create a model to research ODEs, almost all models used are theoretical frameworks, and there are few studies that simulate the operation process of ODEs through mathematical modeling methods.(ii)
The influence of demographic factors (such as the registration of new users and the closure of old accounts) on information diffusion is considered. Most of the papers [18, 19] used closed models to describe ODEs, but in real life, the population in an ODE is not static.(iii)
To better explore the effect of the official guidance release on information diffusion, we classify ODI support groups in the model into rational and irrational disseminators based on their knowledge of the ODI policy due to group force interference. When people are in the same group, a herd mentality will occur among users, and the phenomenon of “Herd Behavior” appears.(iv)
We considered the possibility that some users may change their attitudes in our model. In some specific scenarios, some irrational supporters do not understand the specific policies and content of ODI, so they are easily deceived by negative information from opponents and turn to the opposite attitude. Likewise, some irrational supporters may also become rational supporters after understanding the benefits of the ODI. The possibility of two changes is positively correlated with the number of users in different individuals.This paper is organized as follows: Section2 presents a review and related literature. Section 3 describes the ILSOC model based on the information diffusion model. Section 4 presents the numerical simulations and discusses the experimental results, including its specific measures and suggestions. Section 5 summarizes this paper and offers directions for future work.


## 2. Related Literature

In this section, the work connected to our research is elaborated totally. First of all, define the open data ecosystem, and then, it explains the information diffusion between users. It is clear in all its aspects and offers the exact information needed to prove the results.


### 2.1. ODE

If open data connect different stakeholders in society [4], the ODE connects all kinds of open data in society. The concept of an “ODE” was first proposed by Pollock [20]. He believes that the ODE is a new data usage model that enables the government and other institutions to access their data for the public, and then intermediaries release the processed data products and let them return to the ecosystem in a reusable manner. Harrison et al. make the ODE a social system that must be created in an information-intensive society. It is driven by technology to convey the interdependence of participants, organizations, material infrastructure, and symbolic resources [15]. Reggi believes that the ODE is a self-organizing and evolving system because of feedback and adjustment between participants and data activities. In this system, people using open datasets can strengthen government accountability and promote innovation [21]. From the information technology perspective, Ding et al. defined a linked ODE as a linked database system where stakeholders of different sizes and roles (including government employees, developers, and citizens) can find, manage, archive, publish, reuse, integrate, mash-up, and consume open government data in connection with online tools, services, and societies [22]. An ODE can help citizens search, find, evaluate, view, and obtain permission information related to the data. It can also capture, clean, analyze, enrich, combine, link, and visualize data for explaining, discussing, and then providing feedback to data providers and other stakeholders [23].Despite the various focuses of different studies that lead to different definitions and types of ODEs, the way ecosystems sustainably develop has always been the main subject of research on ODEs and ecology. Sustainability, a power source for ecosystems, is an important element used to assess the health of ODEs [24]. A sustainable ODE can ensure stable operation in emergencies and provide data services and products adequately [15, 25]. Only a sustainable ODE could formulate clearer strategic goals for cities and effectively promote some feedback mechanisms among governments, communities, and citizens [21].Users, as a dominant part of the ODE, are responsible for pushing the ODI action, giving feedback, and supervising the behavior and decision-making of data institutions to realize the added value of open data. In public university governance in South Africa, data users (universities) derive value from the data to build interactive relationships to share the data [26]. If users perceive value in data and are adequately resourced to enter an information exchange relationship, the ecosystem will appear to be more stable and sustainable.


### 2.2. Information Diffusion

In the digital age, the information diffusion between users as an element of the ODI [27] has great effects on the ODE. Information diffusion between users can ensure ecosystem sustainability, especially in terms of information strategies, such as by word of mouth. The ODE framework design must take the information science dimension into consideration [28]. Nevertheless, existing research has not attached sufficient attention to the information diffusion mechanism among users. Researchers are confined to describing the static network structure and neighborhood details in the entire ODE rather than the challenges of dynamic processes leading to information competition. To surmount the limitations above, we adopt the information diffusion model, which was developed from classic infectious disease research to study the dynamic process of user-information diffusion within an ODE.Research on epidemic models is a branch of infectious disease informatics. Since viruses follow certain patterns of spreading, establishing mathematical models can grasp the spreading process of infectious diseases both in time and space, and can simulate and predict the developmental trend of the virus, enabling researchers to seek the optimal strategy for preventing and controlling infectious diseases [29]. Information diffusion between users has a similar processing method to human infectious diseases [30]. When information flows from one individual or community to another, it spreads like a virus (Details on the information diffusion model are provided in Section 3.1). Thus, classic epidemic models (SIS model and SIR model) or other advanced models (SEIR model and SIHR model) are mainly used for inspecting the spread of information. Therefore, the SIR model can be used to study the user-information interaction behavior of ODEs and to describe the process of information diffusion in ecosystems more comprehensively.From the above, it can be concluded that the interaction between users will impact ODE sustainability. In addition, there are few articles describing the dynamic information diffusion process between users. The information diffusion model is used in the next section to study the nodes of users in different stages and the results of diffusion.


## 2.1. ODE

If open data connect different stakeholders in society [4], the ODE connects all kinds of open data in society. The concept of an “ODE” was first proposed by Pollock [20]. He believes that the ODE is a new data usage model that enables the government and other institutions to access their data for the public, and then intermediaries release the processed data products and let them return to the ecosystem in a reusable manner. Harrison et al. make the ODE a social system that must be created in an information-intensive society. It is driven by technology to convey the interdependence of participants, organizations, material infrastructure, and symbolic resources [15]. Reggi believes that the ODE is a self-organizing and evolving system because of feedback and adjustment between participants and data activities. In this system, people using open datasets can strengthen government accountability and promote innovation [21]. From the information technology perspective, Ding et al. defined a linked ODE as a linked database system where stakeholders of different sizes and roles (including government employees, developers, and citizens) can find, manage, archive, publish, reuse, integrate, mash-up, and consume open government data in connection with online tools, services, and societies [22]. An ODE can help citizens search, find, evaluate, view, and obtain permission information related to the data. It can also capture, clean, analyze, enrich, combine, link, and visualize data for explaining, discussing, and then providing feedback to data providers and other stakeholders [23].Despite the various focuses of different studies that lead to different definitions and types of ODEs, the way ecosystems sustainably develop has always been the main subject of research on ODEs and ecology. Sustainability, a power source for ecosystems, is an important element used to assess the health of ODEs [24]. A sustainable ODE can ensure stable operation in emergencies and provide data services and products adequately [15, 25]. Only a sustainable ODE could formulate clearer strategic goals for cities and effectively promote some feedback mechanisms among governments, communities, and citizens [21].Users, as a dominant part of the ODE, are responsible for pushing the ODI action, giving feedback, and supervising the behavior and decision-making of data institutions to realize the added value of open data. In public university governance in South Africa, data users (universities) derive value from the data to build interactive relationships to share the data [26]. If users perceive value in data and are adequately resourced to enter an information exchange relationship, the ecosystem will appear to be more stable and sustainable.


## 2.2. Information Diffusion

In the digital age, the information diffusion between users as an element of the ODI [27] has great effects on the ODE. Information diffusion between users can ensure ecosystem sustainability, especially in terms of information strategies, such as by word of mouth. The ODE framework design must take the information science dimension into consideration [28]. Nevertheless, existing research has not attached sufficient attention to the information diffusion mechanism among users. Researchers are confined to describing the static network structure and neighborhood details in the entire ODE rather than the challenges of dynamic processes leading to information competition. To surmount the limitations above, we adopt the information diffusion model, which was developed from classic infectious disease research to study the dynamic process of user-information diffusion within an ODE.Research on epidemic models is a branch of infectious disease informatics. Since viruses follow certain patterns of spreading, establishing mathematical models can grasp the spreading process of infectious diseases both in time and space, and can simulate and predict the developmental trend of the virus, enabling researchers to seek the optimal strategy for preventing and controlling infectious diseases [29]. Information diffusion between users has a similar processing method to human infectious diseases [30]. When information flows from one individual or community to another, it spreads like a virus (Details on the information diffusion model are provided in Section 3.1). Thus, classic epidemic models (SIS model and SIR model) or other advanced models (SEIR model and SIHR model) are mainly used for inspecting the spread of information. Therefore, the SIR model can be used to study the user-information interaction behavior of ODEs and to describe the process of information diffusion in ecosystems more comprehensively.From the above, it can be concluded that the interaction between users will impact ODE sustainability. In addition, there are few articles describing the dynamic information diffusion process between users. The information diffusion model is used in the next section to study the nodes of users in different stages and the results of diffusion.


## 3. The Proposed Model: ILSOC Information Diffusion Model

### 3.1. Classic SIR Model

Kermack and McKendrick divided the regional population into three groups: susceptible individuals, infected individuals, and recovered individuals. First, they used differential equations to model the dynamics of infection between different individuals [31]. The SIR (susceptible-infected-recovered) model established subsequently became a classic method for quantitative research on epidemics. There are two processes of the three individuals in the SIR model: the first stage is when a susceptible person (S) will have a certain probability a when they contact an infected person (I) to become an infected person (I). The second stage occurs when an infected person (I) will have a certain probability b after treatment of becoming a recovered person (R).As shown in Figure1, the dynamic process of the progressing epidemic can be mapped to information diffusion in the SIR epidemic model. When a susceptible individual (S) receives the information, there is a certain probability c of becoming an infected individual (I). This process corresponds to virus infection, as in the first stage above. An infected individual (I) will have a certain probability d of removing the message and becoming a recovered person (R), which can map to the process of recovery from an epidemic, as in the second stage above.Figure 1
The process of the SIR model.


### 3.2. The ILSOC Model

According to the SIR model, we can describe the process of information diffusion between users in the ODE and build the ILSOC model. It is the new model that is defined in this paper and works properly and makes efficient results. In accordance with reality, ODE users can be divided into two opposite states according to their attitudes about the ODI, namely, its supporters and opponents. Concurrently, given that personality traits affect different beliefs, supporters are divided into two groups, rational and irrational groups, based on whether they know the true ODI policy or not. Therefore, there are six states of persons in the model, includingI(t) (ignorant users who are unaware of the ODI), L(t) (latent users who are easily affected by any information), S1(t) (the ODI rational supporters who understand the policy and diffuse positive information), S2(t) (the ODI irrational supporters who do not understand the policy but still diffuse positive information), O(t) (the ODI opponents who diffuse negative information), and C(t) (calm users who lose interest and no longer diffuse any information). The transformation between each different user is depicted in Figure 2. We let N(t) represent the total population in the ecosystem at time t; Then, we can obtain the equation as follows:(1)Nt=It+Lt+S1t+S2t+Ot+Ct,It,Lt,S1t,S2t,Ot,Ct≥0.Figure 2
The transfer diagram of the ILSOC model.According to the ILSOC model in Figure2, the rules of information diffusion described in the model can be summarized as follows:(1)
Due to the openness and the dynamics of the ODE, this model has a variable population scale. It is assumed that all new users enter the ignorant class with a constantε (i.e., immigration rate), and all existing users migrate out of the six categories at a constant ρ (i.e., emigration rate).(2)
When in contact with an ODI opponent, an ignorant becomes latent with probabilityφ as the opponent contact rate.(3)
When in contact with an ODI supporter, neither rational nor irrational, an ignorant becomes latent with the probability called the supporters-contacting rate (μ1 or μ2). Although μ1 and μ2 are both called the support contact rate, there are essential differences between the two. μ1 represents ignorant users converting latent users after receiving effective information provided by rational supporters, while μ2 means that ignorant users convert latent users due to herd mentality.As mentioned above, ODI supporters and opponents usually exist in ODEs at the same time, which means that ignorant users receive two types of information and then turn into latent categories. Ignorant users may be affected by information from different categories, but some latent users may not be able to make accurate judgments when they are facing two contradictory pieces of information. In addition, even if some ignorant users have only received positive information, they may still forward negative information by personal emotional tendencies and psychological appearances. Similarly, latent users may become supporters after being affected by negative information [32]. Therefore, there is no difference between users in the latent category whether they receive information from supporters or opponents. Due to the abovementioned factors, we consider that latent users will have three different attitudes about ODI: supporters, opponents, and calm users with a positive conversation rate, a negative conversation rate, and a silent rate, respectively. These attitudes can be defined as follows:(1)
Some latent users may be inclined to believe in the negative information and turn into ODI opponents with a negative-conversing rateβ.(2)
Some latent users may be inclined to believe positive information and turn into ODI supporters with a positive-conversing rateα1 or α2. The positive-rational-conversing rate α1 represents latent users who believe in the benefits of the ODI after clarifying the content and policies before becoming a rational supporter. The positive-irrational-conversing rate α2 represents latent users who do not understand the actual content and then turn into an irrational supporters due to herd mentality.(3)
Some latent users may not be interested in all of the information that they receive and will remain silent forever. In this case, they will become calm users at the latent-silent rateγ.(4)
Considering the evolution law of information, some rational supporters, irrational supporters, and opponents may spontaneously lose interest in any information over time, and they will turn into silent users with rational-silent rateδ1, irrational-silent rate δ2 and opposite-silent rate θ.Inside the ecosystem, there are not only transformations caused by the exposure of users to different groups but also transformations caused by external factors. Thus, some interaction occurs between the ODI rational supporters, the irrational supporters, and the opponents:(1)
After receiving official information or new policies about the ODI, some opponents may realize the error of their previous views and turn into ODI irrational supporters with a positive-reversal rate m.(2)
On the one hand, some irrational supporters may become opponents with a negative reversal raten after they receive negative information due to their vacillating attitude. On the other hand, some irrational supporters may become rational supporters with a rational-reversal rate ξ after they learn about the specific policies of the ODI.By referring to the existing methods for constructing the dynamic equations of information transmission, the differential equation model of system dynamics represents the ILSOC model as follows:(2)dItdt=ε−μ1S1tIt−μ2S2tIt−φOtIt−ρItdLtdt=μ1S1tIt+μ2S2tIt+φOtIt−α1+α2+β+γ+ρLtdS1tdt=α1Lt+ξS2t−ρ+δ1S1tdS1tdt=α2Lt+mOt−δ2+n+ρ+ξS2tdOtdt=βLt+nS2t−θ+m+ρOtdCtdt=δ1S1t+δ2S2t+γLt+θOt−ρCt..


### 3.3. ILSOC Model Stability Point

To find the stable point of the model, we combined (1) and (2) to obtain the following:(3)dNtdt=dItdt+dLtdt+dS1tdt+dS2tdt+dOtdt+dCtdt=ε−ρNt.After integrating both sides of (3), it is easy to know that Nt=N0−ε/ρe−ρt+ε/ρ and N0=I0+L0+S10+S20+O0+C0; thus, limt⟶+∞Nt=limt⟶+∞N0−ε/ρe−ρt+ε/ρ=ε/ρ. We let R6+ denote the nonnegative cone and its lower dimensional faces. The model can be studied in the feasible region of Ω=I,L,S1,S2,O,C∈R6+, 0≤I+L+S1+S2+O+C≤ε/ρ.Clearly,C(t) is independent of the system of differential equations about I(t), L(t), S1(t), S2(t), O(t), so the system of ordinary differential equations about them can be solved without considering C(t) as follows:(4)dItdt=ε−μ1S1tIt−μ2S2tIt−φOtIt−ρItdLtdt=μ1S1tIt+μ2S2tIt+φOtIt−α1+α2+β+γ+ρLtdS1tdt=α1Lt+ξS2t−ρ+δ1S1tdS1tdt=α2Lt+mOt−δ2+n+ρ+ξS2tdOtdt=βLt+nS2t−θ+m+ρOt..First, the existence of the equilibrium point of equations should be analyzed, and thus, we set the value of the left side of equation (4) to 0 to generate a new equation system as follows:(5)ε−μ1S1I−μ2S2I−φOI−ρI=0μ1S1I+μ2S2I+φOI−α1+α2+β+γ+ρL=0α1L+ξS2−ρ+δ1S1=0α2L+mO−δ2+n+ρ+ξS2=0βL+nS2−θ+m+ρO=0..Then, solving (5), two equilibrium points of this model are found. The information demise point is Φ0=ε/ρ,0,0,0,0, and the information diffusion point is Φ∗=I∗,L∗,S1∗,S2∗,O∗, with the following:(6)I∗=nρ+δ1α1+α2+β+γ+ρδ2+n+ρ+ξ−mω1+ω2−ω3+ω4L∗=ε−ρI∗α1+α2+β+γ+ρS1∗=α1L∗+ξS2∗δ2+n+ρ+ξS2∗=α2ρ+θ+mL∗nδ2+n+ρ+ξ−m−βnO∗=α2L∗δ2+n+ρ+ξ−m.,ω1=μ1α1n−βξδ2+n+ρ+ξ−m;ω2=α2ρ+θ+mμ1ξ+μ2ρ+μ2δ1,ω3=μ2βρ+δ1ρ+δ1+n+ξ−m;ω4=α2φnρ+δ1.According to the rules of the information diffusion model, when the number of latent users is less than 0, the internal information of the system will no longer be transmitted [33]. When L∗=ε−ρI∗/α1+α2+β+γ+ρ〉0 and α1+α2+β+γ+ρ〉0, the threshold parameter R0=ε/ρ⋅1/I∗ can be calculated.The number of equilibria can be determined byR0: if R0〈1, there is no nonzero equilibrium point in the region Ω, and the equilibrium point is stable only when it is at the extinction equilibrium point Φ0. If R0〈1, there is a unique information-diffusion equilibrium in Ω.


## 3.1. Classic SIR Model

Kermack and McKendrick divided the regional population into three groups: susceptible individuals, infected individuals, and recovered individuals. First, they used differential equations to model the dynamics of infection between different individuals [31]. The SIR (susceptible-infected-recovered) model established subsequently became a classic method for quantitative research on epidemics. There are two processes of the three individuals in the SIR model: the first stage is when a susceptible person (S) will have a certain probability a when they contact an infected person (I) to become an infected person (I). The second stage occurs when an infected person (I) will have a certain probability b after treatment of becoming a recovered person (R).As shown in Figure1, the dynamic process of the progressing epidemic can be mapped to information diffusion in the SIR epidemic model. When a susceptible individual (S) receives the information, there is a certain probability c of becoming an infected individual (I). This process corresponds to virus infection, as in the first stage above. An infected individual (I) will have a certain probability d of removing the message and becoming a recovered person (R), which can map to the process of recovery from an epidemic, as in the second stage above.Figure 1
The process of the SIR model.


## 3.2. The ILSOC Model

According to the SIR model, we can describe the process of information diffusion between users in the ODE and build the ILSOC model. It is the new model that is defined in this paper and works properly and makes efficient results. In accordance with reality, ODE users can be divided into two opposite states according to their attitudes about the ODI, namely, its supporters and opponents. Concurrently, given that personality traits affect different beliefs, supporters are divided into two groups, rational and irrational groups, based on whether they know the true ODI policy or not. Therefore, there are six states of persons in the model, includingI(t) (ignorant users who are unaware of the ODI), L(t) (latent users who are easily affected by any information), S1(t) (the ODI rational supporters who understand the policy and diffuse positive information), S2(t) (the ODI irrational supporters who do not understand the policy but still diffuse positive information), O(t) (the ODI opponents who diffuse negative information), and C(t) (calm users who lose interest and no longer diffuse any information). The transformation between each different user is depicted in Figure 2. We let N(t) represent the total population in the ecosystem at time t; Then, we can obtain the equation as follows:(1)Nt=It+Lt+S1t+S2t+Ot+Ct,It,Lt,S1t,S2t,Ot,Ct≥0.Figure 2
The transfer diagram of the ILSOC model.According to the ILSOC model in Figure2, the rules of information diffusion described in the model can be summarized as follows:(1)
Due to the openness and the dynamics of the ODE, this model has a variable population scale. It is assumed that all new users enter the ignorant class with a constantε (i.e., immigration rate), and all existing users migrate out of the six categories at a constant ρ (i.e., emigration rate).(2)
When in contact with an ODI opponent, an ignorant becomes latent with probabilityφ as the opponent contact rate.(3)
When in contact with an ODI supporter, neither rational nor irrational, an ignorant becomes latent with the probability called the supporters-contacting rate (μ1 or μ2). Although μ1 and μ2 are both called the support contact rate, there are essential differences between the two. μ1 represents ignorant users converting latent users after receiving effective information provided by rational supporters, while μ2 means that ignorant users convert latent users due to herd mentality.As mentioned above, ODI supporters and opponents usually exist in ODEs at the same time, which means that ignorant users receive two types of information and then turn into latent categories. Ignorant users may be affected by information from different categories, but some latent users may not be able to make accurate judgments when they are facing two contradictory pieces of information. In addition, even if some ignorant users have only received positive information, they may still forward negative information by personal emotional tendencies and psychological appearances. Similarly, latent users may become supporters after being affected by negative information [32]. Therefore, there is no difference between users in the latent category whether they receive information from supporters or opponents. Due to the abovementioned factors, we consider that latent users will have three different attitudes about ODI: supporters, opponents, and calm users with a positive conversation rate, a negative conversation rate, and a silent rate, respectively. These attitudes can be defined as follows:(1)
Some latent users may be inclined to believe in the negative information and turn into ODI opponents with a negative-conversing rateβ.(2)
Some latent users may be inclined to believe positive information and turn into ODI supporters with a positive-conversing rateα1 or α2. The positive-rational-conversing rate α1 represents latent users who believe in the benefits of the ODI after clarifying the content and policies before becoming a rational supporter. The positive-irrational-conversing rate α2 represents latent users who do not understand the actual content and then turn into an irrational supporters due to herd mentality.(3)
Some latent users may not be interested in all of the information that they receive and will remain silent forever. In this case, they will become calm users at the latent-silent rateγ.(4)
Considering the evolution law of information, some rational supporters, irrational supporters, and opponents may spontaneously lose interest in any information over time, and they will turn into silent users with rational-silent rateδ1, irrational-silent rate δ2 and opposite-silent rate θ.Inside the ecosystem, there are not only transformations caused by the exposure of users to different groups but also transformations caused by external factors. Thus, some interaction occurs between the ODI rational supporters, the irrational supporters, and the opponents:(1)
After receiving official information or new policies about the ODI, some opponents may realize the error of their previous views and turn into ODI irrational supporters with a positive-reversal rate m.(2)
On the one hand, some irrational supporters may become opponents with a negative reversal raten after they receive negative information due to their vacillating attitude. On the other hand, some irrational supporters may become rational supporters with a rational-reversal rate ξ after they learn about the specific policies of the ODI.By referring to the existing methods for constructing the dynamic equations of information transmission, the differential equation model of system dynamics represents the ILSOC model as follows:(2)dItdt=ε−μ1S1tIt−μ2S2tIt−φOtIt−ρItdLtdt=μ1S1tIt+μ2S2tIt+φOtIt−α1+α2+β+γ+ρLtdS1tdt=α1Lt+ξS2t−ρ+δ1S1tdS1tdt=α2Lt+mOt−δ2+n+ρ+ξS2tdOtdt=βLt+nS2t−θ+m+ρOtdCtdt=δ1S1t+δ2S2t+γLt+θOt−ρCt..


## 3.3. ILSOC Model Stability Point

To find the stable point of the model, we combined (1) and (2) to obtain the following:(3)dNtdt=dItdt+dLtdt+dS1tdt+dS2tdt+dOtdt+dCtdt=ε−ρNt.After integrating both sides of (3), it is easy to know that Nt=N0−ε/ρe−ρt+ε/ρ and N0=I0+L0+S10+S20+O0+C0; thus, limt⟶+∞Nt=limt⟶+∞N0−ε/ρe−ρt+ε/ρ=ε/ρ. We let R6+ denote the nonnegative cone and its lower dimensional faces. The model can be studied in the feasible region of Ω=I,L,S1,S2,O,C∈R6+, 0≤I+L+S1+S2+O+C≤ε/ρ.Clearly,C(t) is independent of the system of differential equations about I(t), L(t), S1(t), S2(t), O(t), so the system of ordinary differential equations about them can be solved without considering C(t) as follows:(4)dItdt=ε−μ1S1tIt−μ2S2tIt−φOtIt−ρItdLtdt=μ1S1tIt+μ2S2tIt+φOtIt−α1+α2+β+γ+ρLtdS1tdt=α1Lt+ξS2t−ρ+δ1S1tdS1tdt=α2Lt+mOt−δ2+n+ρ+ξS2tdOtdt=βLt+nS2t−θ+m+ρOt..First, the existence of the equilibrium point of equations should be analyzed, and thus, we set the value of the left side of equation (4) to 0 to generate a new equation system as follows:(5)ε−μ1S1I−μ2S2I−φOI−ρI=0μ1S1I+μ2S2I+φOI−α1+α2+β+γ+ρL=0α1L+ξS2−ρ+δ1S1=0α2L+mO−δ2+n+ρ+ξS2=0βL+nS2−θ+m+ρO=0..Then, solving (5), two equilibrium points of this model are found. The information demise point is Φ0=ε/ρ,0,0,0,0, and the information diffusion point is Φ∗=I∗,L∗,S1∗,S2∗,O∗, with the following:(6)I∗=nρ+δ1α1+α2+β+γ+ρδ2+n+ρ+ξ−mω1+ω2−ω3+ω4L∗=ε−ρI∗α1+α2+β+γ+ρS1∗=α1L∗+ξS2∗δ2+n+ρ+ξS2∗=α2ρ+θ+mL∗nδ2+n+ρ+ξ−m−βnO∗=α2L∗δ2+n+ρ+ξ−m.,ω1=μ1α1n−βξδ2+n+ρ+ξ−m;ω2=α2ρ+θ+mμ1ξ+μ2ρ+μ2δ1,ω3=μ2βρ+δ1ρ+δ1+n+ξ−m;ω4=α2φnρ+δ1.According to the rules of the information diffusion model, when the number of latent users is less than 0, the internal information of the system will no longer be transmitted [33]. When L∗=ε−ρI∗/α1+α2+β+γ+ρ〉0 and α1+α2+β+γ+ρ〉0, the threshold parameter R0=ε/ρ⋅1/I∗ can be calculated.The number of equilibria can be determined byR0: if R0〈1, there is no nonzero equilibrium point in the region Ω, and the equilibrium point is stable only when it is at the extinction equilibrium point Φ0. If R0〈1, there is a unique information-diffusion equilibrium in Ω.


## 4. Numerical Simulations and Discussion

To determine how the number and structure of users in the ODE are affected by information diffusion behaviors among users inside and to verify the analysis results of the ILSOC model, we perform a numerical simulation. This enables us to find a further way that can truly make the ODE sustainable from the users’ perspectives.


### 4.1. Simulation Analysis of a Benchmark Model

Assuming that the total population at timet0 is 1,000 and one rational supporter of the ODI and one opponent of the ODI diffuse the information in this ecosystem, the rest of the users know nothing about the ODI. Then, N(0) = 1,0000, I(0) = 9998, L(0) = 0, S1(0) = 1, S2(0) = 0, O(0) = 1, C(0) = 0. Figure 3 and 4 verify the theoretical analysis in Section 3.3.Figure 3
WhenR0 = 0.2026 < 1, the number of users over time (t) with ε = 0.1, ρ = 0.01, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.001, α2 = 0.001, β = 0.001, θ = 0.02, δ1 = 0.002, δ2 = 0.002, ξ = 0.001, (m) = 0.0001, (n) = 0.001, γ = 0.001.Figure 4
WhenR0 = 8.2056 > 1, the number of users over time (t) with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002.The way that the number of the six classes of users changes over timet is shown in Figure 3 with R0 < 1. The trend shown in the figure expresses that the number of ignorant users will continuously decline throughout the propagation process until it is zero. The number of latent users rises first, then reaches its peak, and finally drops to zero, indicating that the information about the ODI will disappear after the system reaches a steady state. Moreover, it can be observed that the changing trends of supporters, opponents, and calm users have almost no change, and their values are basically zero.The way that the number of the six classes of users changes over timet is seen in Figure 4 with R0 > 1. As shown in this figure, the number of ignorant users and latent users have the same trend as in Figure 3, but they change faster in Figure 4. The number of rational supporters during the entire propagation process reaches a peak after rising in the initial stage and finally stabilizes after falling to an equilibrium value. The number of irrational supporters continuously increases and ultimately reaches a steady value. The number of opponents and calm users has a similar trend to rational supporters.In Figures3 and 4, the information diffusion process in the ODE will follow the basic laws of three phases: rising, peaking, and falling. However, when the ODE is active, the number of ignorant users and latent users changes faster and finally floods with many calm users, some rational and irrational supporters, and opponents. When in a state of extinction, this ecosystem will lose all users and eventually die.In addition, we specifically downloaded the number of people who have searched the ODE Platform in Chinese provinces on the Baidu search engine to observe the number of latent users, which is the most crucial index to reflect the effectiveness of information diffusion. As shown in Figure5, the blue dots represent the data. The real data (blue spots) are mostly consistent with the computed results (red line), verifying the accuracy of our proposed model. Therefore, in the next section, we analyze the way to ensure the balance of information spread through mutual contact between users when the ODE is active and promote the sustainable development of the ODE.Figure 5
Comparison of the number of latent users that were informed by the simulation and theoretical results.


### 4.2. Sustainability Analysis of the ODEs from the User’s Point of View

When the ODE is active (R0 > 1), the disturbances caused by different factors among the rational supporters (S1(t)), the irrational supporters (S2(t)), and the opponents (O(t)) enable us to understand how to adjust the interaction between users within the ODE in the future. Next, we analyze the influence of the different user-contacting rates.


#### 4.2.1. The Impact of Users-Contacting Rate

Figure6 and 7 describe that the number of ODI rational supporters, irrational supporters, and opponents changes with different supporter contact rates over time t. In general, the larger the supporter contact rate is, the greater the number of users in the three groups, and they will reach the peak faster. However, there is a fact that should be mentioned. On the one hand, there is a greater increase in the supporter contact rate from 0.02 to 0.2. However, rational supporters and opponents will not change considerably when they reach a stable state. On the other hand, when the supporter contact rate increases, the number of opponents in the early period will rise, but the time to reach the peak and decline will be dramatically earlier.Figure 6
Number of rational supporters, irrational supporters, and opponents versus time-varying over different supporter contact ratesμ1 with ε = 1, ρ = 0.005, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 7
Number of rational supporters, irrational supporters, and opponents versus time varying over different supporter contact ratesμ2 with ε = 1, ρ = 0.005, μ1 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure8 depicts the number of rational supporters, irrational supporters, and opponents with different opponent contact rates φ. The changing trends of the three types under different φ are similar to the above changing trends. When the opponent contact rate decreases to a low level, such as 0.00002 to 0.000002, the number of supporters and opponents does not change substantially.Figure 8
Number of rational supporters, irrational supporters, and opponents versus time varying over different opponent contact ratesφ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)In summary, when users are in a high supporter contact rate area, more ignorant users would contact supporters and turn into latent users. This also leads to more latent users becoming opponents, causing the number of opponents to increase considerably. When there are users in a low opponent contact rate area, the number of opponents has no substantial decline, but the proportion of supporters decreases. Based on this, the internal organization of the ecosystem should control the correct development direction. If they only blindly use their power to control the user contact rate, it will not turn more ignorant users into supporters, but it will be counterproductive.


#### 4.2.2. The Impact of the Users-Conversing Rate

Figure9, 10, and 11 demonstrate the number of ODI rational supporters, irrational supporters, and opponents over time t with different user conversion rates. Three interesting phenomena are discovered:Figure 9
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive-rational-conversing ratesα1 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 10
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive-irrational-conversing ratesα2 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 11
Number of rational supporters, irrational supporters, and opponents versus time varying over different negative-conversing ratesβ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)First, with the increase in the positive-rational-conversing rateα1, although the number of supporters is boosting, they are still maintained at a very low level after the system is balanced. Moreover, as the negative conversion rate β decreases, the number of opponents cannot be reduced, which is inconsistent with our common sense. Second, the number of rational supporters, irrational supporters, and opponents will increase due to the increase in the positive-irrational-conversing rate α2. However, the number of opponents has gradually increased after system stabilization, but its peak has been continuously decreasing. Third, with the decrease in β, the peak of the opponent group rapidly decreases, but the number of opponents in the balanced stage gradually increases. Meanwhile, the number of supporters changes very slightly after β is reduced to a certain level (0.0005 to 0.0001).One possible explanation is that as the negative-conversing rateβ decreases, although the number of latent users directly becoming opponents decreases, more latent users will turn into irrational supporters due to their “swing” characteristic, and then more irrational supporters will turn into opponents, which increases the number of opponents indirectly. The phenomenon caused by α1 is the same as the effect brought by β. In addition, this also explains why the numbers of the three groups will increase as α2 increases.Due to the above, organizations in the ODE need to take actions to increase publicity within a controllable range, and thus, more potential users can truly understand the true content of the ODI. Organizations can also use advanced technology to analyze the emotional tendencies and psychological attractiveness of users. They can also formulate and publish more targeted policies to make users truly trust the convenience and benefits brought by the ODE. In this way, the number of irrational supporters and opponents could be reduced.


#### 4.2.3. The Impact of the Silent Rate

Figure12 illustrates the rational supporters, irrational supporters, and opponents under different latent-silent rates γ over time t. As the value of γ gradually increases, the number of rational supporters, irrational supporters, and opponents considerably drops, and its peak falls off a cliff. A larger value of γ means that more ignorant users skip the information diffusion stage, and they do not participate in any data activities in the ODE.Figure 12
Number of rational supporters, irrational supporters, and opponents versus time varying over different latent-silent ratesγ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure13, 14 and 15 describe the ODI rational supporters, irrational supporters, and opponents, respectively, under different silence rates over time t.Figure 13
Number of rational supporters, irrational supporters, and opponents versus time varying over different rational-silent ratδ1 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 14
Number of rational supporters, irrational supporters, and opponents versus time varying over different irrational silence ratesδ2 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 15
Number of rational supporters, irrational supporters, and opponents versus time varying over different opposite-silence ratesθ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Observing Figures13 and 14, we can find that when the rational-silent rate δ1 increases, only the number of rational supporters decreases, and the number of irrational supporters and opponents does not show any substantial change. When the irrational-silent rate δ2 increases, the number of rational supporters and irrational supporters decreases, while the number of opponents still does not show any obvious changes.In Figure15, comparing the trend of the opponent-silent rate θ with δ1 and δ2, we can find that even a small fluctuation of θ would have a severe impact on rational supporters, irrational supporters, and opponents. The number of rational and irrational supporters increases with the continuous increase of θ, while the number of opponents decreases. Moreover, when θ increases from a lower level to a higher level, although the peak of opponents will plummet, in contrast, the number of rational supporters after the system is balanced reaches a high level, which is exactly what we expect.It can be concluded thatθ severely disturbs the number of users in the ODE. When θ is larger, more opponents will stop spreading negative information and turn into silent users. As a result, the proportion of supporters in this ecosystem increases continually, and ignorant users will have a greater probability of contacting supporters. Thus, more users begin to support the ODI and become internal supporters. To maintain the health of the ODE and promote its sustainable development, internal organizations or other stakeholders should pay close attention to the conversion trends of latent users, reduce the direct conversion of latent users into silent users, and make more users participate in the data activities. In addition, organizations also need to take effective measures to guide users. Then, they can create a positive atmosphere within the ecosystem space to put pressure on opponents. Additionally, they also need to establish appropriate rewards or punishments to increase the opponent-silent rate.


#### 4.2.4. The Impact of the Reversal Rate

Figure16, 17 and 18 present the ODI rational supporters, irrational supporters, and opponents, respectively, under different reversal rates ξ, m, or n over time t. Overall, the interaction between the three has some impact on the structure of the ODE, but the reversal rate disturbs the number of rational and irrational supporters more severely, while the impact on the change in the number of opponents is not obvious.Figure 16
Number of rational supporters, irrational supporters, and opponents versus time varying over different rational reversal ratesξ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 17
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive reversal rates (m) withε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 18
Number of rational supporters, irrational supporters, and opponents versus time varying over different negative reversal rates (n) withε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)As the rational reversal rateξ increases, the number of rational supporters gradually increases, while the number of irrational supporters gradually decreases due to the transformation of irrational supporters to rational supporters. When ξ increased to a higher level (from 0.001 to 0.01), the number of rational and irrational supporters dropped sharply, while the fluctuations in the number of opponents were not as substantial as those of the supporters.As the positive reversal ratem increases, the numbers of both rational supporters and irrational supporters show a growing trend and remain at a high level after the system reaches equilibrium, while the number of opponents basically remains at a low level. Similarly, as the negative reversal rate n gradually decreases, the number of rational and irrational supporters also shows a considerable increasing trend, but the number of opponents is still at a low level. It is easy to understand that as m increases or n decreases, more opponents will become supporters (whether rational or irrational), which leads to a reduction in the exposure of ignorant users to negative information and a direct decrease in the total number of opponents.In response to the above simulation results, internal organizations and other stakeholders in the ODE should focus on how to convert ODI opponents. For example, official agencies can counter negative information by publishing authoritative information, and thus, more opponents can understand the actual policies and benefits of the ODI. The organization should also enhance data transparency to respond to the negative attitude of the opponents, thereby awakening the opponents to support the ODI.


## 4.1. Simulation Analysis of a Benchmark Model

Assuming that the total population at timet0 is 1,000 and one rational supporter of the ODI and one opponent of the ODI diffuse the information in this ecosystem, the rest of the users know nothing about the ODI. Then, N(0) = 1,0000, I(0) = 9998, L(0) = 0, S1(0) = 1, S2(0) = 0, O(0) = 1, C(0) = 0. Figure 3 and 4 verify the theoretical analysis in Section 3.3.Figure 3
WhenR0 = 0.2026 < 1, the number of users over time (t) with ε = 0.1, ρ = 0.01, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.001, α2 = 0.001, β = 0.001, θ = 0.02, δ1 = 0.002, δ2 = 0.002, ξ = 0.001, (m) = 0.0001, (n) = 0.001, γ = 0.001.Figure 4
WhenR0 = 8.2056 > 1, the number of users over time (t) with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002.The way that the number of the six classes of users changes over timet is shown in Figure 3 with R0 < 1. The trend shown in the figure expresses that the number of ignorant users will continuously decline throughout the propagation process until it is zero. The number of latent users rises first, then reaches its peak, and finally drops to zero, indicating that the information about the ODI will disappear after the system reaches a steady state. Moreover, it can be observed that the changing trends of supporters, opponents, and calm users have almost no change, and their values are basically zero.The way that the number of the six classes of users changes over timet is seen in Figure 4 with R0 > 1. As shown in this figure, the number of ignorant users and latent users have the same trend as in Figure 3, but they change faster in Figure 4. The number of rational supporters during the entire propagation process reaches a peak after rising in the initial stage and finally stabilizes after falling to an equilibrium value. The number of irrational supporters continuously increases and ultimately reaches a steady value. The number of opponents and calm users has a similar trend to rational supporters.In Figures3 and 4, the information diffusion process in the ODE will follow the basic laws of three phases: rising, peaking, and falling. However, when the ODE is active, the number of ignorant users and latent users changes faster and finally floods with many calm users, some rational and irrational supporters, and opponents. When in a state of extinction, this ecosystem will lose all users and eventually die.In addition, we specifically downloaded the number of people who have searched the ODE Platform in Chinese provinces on the Baidu search engine to observe the number of latent users, which is the most crucial index to reflect the effectiveness of information diffusion. As shown in Figure5, the blue dots represent the data. The real data (blue spots) are mostly consistent with the computed results (red line), verifying the accuracy of our proposed model. Therefore, in the next section, we analyze the way to ensure the balance of information spread through mutual contact between users when the ODE is active and promote the sustainable development of the ODE.Figure 5
Comparison of the number of latent users that were informed by the simulation and theoretical results.


## 4.2. Sustainability Analysis of the ODEs from the User’s Point of View

When the ODE is active (R0 > 1), the disturbances caused by different factors among the rational supporters (S1(t)), the irrational supporters (S2(t)), and the opponents (O(t)) enable us to understand how to adjust the interaction between users within the ODE in the future. Next, we analyze the influence of the different user-contacting rates.


### 4.2.1. The Impact of Users-Contacting Rate

Figure6 and 7 describe that the number of ODI rational supporters, irrational supporters, and opponents changes with different supporter contact rates over time t. In general, the larger the supporter contact rate is, the greater the number of users in the three groups, and they will reach the peak faster. However, there is a fact that should be mentioned. On the one hand, there is a greater increase in the supporter contact rate from 0.02 to 0.2. However, rational supporters and opponents will not change considerably when they reach a stable state. On the other hand, when the supporter contact rate increases, the number of opponents in the early period will rise, but the time to reach the peak and decline will be dramatically earlier.Figure 6
Number of rational supporters, irrational supporters, and opponents versus time-varying over different supporter contact ratesμ1 with ε = 1, ρ = 0.005, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 7
Number of rational supporters, irrational supporters, and opponents versus time varying over different supporter contact ratesμ2 with ε = 1, ρ = 0.005, μ1 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure8 depicts the number of rational supporters, irrational supporters, and opponents with different opponent contact rates φ. The changing trends of the three types under different φ are similar to the above changing trends. When the opponent contact rate decreases to a low level, such as 0.00002 to 0.000002, the number of supporters and opponents does not change substantially.Figure 8
Number of rational supporters, irrational supporters, and opponents versus time varying over different opponent contact ratesφ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)In summary, when users are in a high supporter contact rate area, more ignorant users would contact supporters and turn into latent users. This also leads to more latent users becoming opponents, causing the number of opponents to increase considerably. When there are users in a low opponent contact rate area, the number of opponents has no substantial decline, but the proportion of supporters decreases. Based on this, the internal organization of the ecosystem should control the correct development direction. If they only blindly use their power to control the user contact rate, it will not turn more ignorant users into supporters, but it will be counterproductive.


### 4.2.2. The Impact of the Users-Conversing Rate

Figure9, 10, and 11 demonstrate the number of ODI rational supporters, irrational supporters, and opponents over time t with different user conversion rates. Three interesting phenomena are discovered:Figure 9
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive-rational-conversing ratesα1 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 10
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive-irrational-conversing ratesα2 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 11
Number of rational supporters, irrational supporters, and opponents versus time varying over different negative-conversing ratesβ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)First, with the increase in the positive-rational-conversing rateα1, although the number of supporters is boosting, they are still maintained at a very low level after the system is balanced. Moreover, as the negative conversion rate β decreases, the number of opponents cannot be reduced, which is inconsistent with our common sense. Second, the number of rational supporters, irrational supporters, and opponents will increase due to the increase in the positive-irrational-conversing rate α2. However, the number of opponents has gradually increased after system stabilization, but its peak has been continuously decreasing. Third, with the decrease in β, the peak of the opponent group rapidly decreases, but the number of opponents in the balanced stage gradually increases. Meanwhile, the number of supporters changes very slightly after β is reduced to a certain level (0.0005 to 0.0001).One possible explanation is that as the negative-conversing rateβ decreases, although the number of latent users directly becoming opponents decreases, more latent users will turn into irrational supporters due to their “swing” characteristic, and then more irrational supporters will turn into opponents, which increases the number of opponents indirectly. The phenomenon caused by α1 is the same as the effect brought by β. In addition, this also explains why the numbers of the three groups will increase as α2 increases.Due to the above, organizations in the ODE need to take actions to increase publicity within a controllable range, and thus, more potential users can truly understand the true content of the ODI. Organizations can also use advanced technology to analyze the emotional tendencies and psychological attractiveness of users. They can also formulate and publish more targeted policies to make users truly trust the convenience and benefits brought by the ODE. In this way, the number of irrational supporters and opponents could be reduced.


### 4.2.3. The Impact of the Silent Rate

Figure12 illustrates the rational supporters, irrational supporters, and opponents under different latent-silent rates γ over time t. As the value of γ gradually increases, the number of rational supporters, irrational supporters, and opponents considerably drops, and its peak falls off a cliff. A larger value of γ means that more ignorant users skip the information diffusion stage, and they do not participate in any data activities in the ODE.Figure 12
Number of rational supporters, irrational supporters, and opponents versus time varying over different latent-silent ratesγ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure13, 14 and 15 describe the ODI rational supporters, irrational supporters, and opponents, respectively, under different silence rates over time t.Figure 13
Number of rational supporters, irrational supporters, and opponents versus time varying over different rational-silent ratδ1 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 14
Number of rational supporters, irrational supporters, and opponents versus time varying over different irrational silence ratesδ2 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 15
Number of rational supporters, irrational supporters, and opponents versus time varying over different opposite-silence ratesθ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Observing Figures13 and 14, we can find that when the rational-silent rate δ1 increases, only the number of rational supporters decreases, and the number of irrational supporters and opponents does not show any substantial change. When the irrational-silent rate δ2 increases, the number of rational supporters and irrational supporters decreases, while the number of opponents still does not show any obvious changes.In Figure15, comparing the trend of the opponent-silent rate θ with δ1 and δ2, we can find that even a small fluctuation of θ would have a severe impact on rational supporters, irrational supporters, and opponents. The number of rational and irrational supporters increases with the continuous increase of θ, while the number of opponents decreases. Moreover, when θ increases from a lower level to a higher level, although the peak of opponents will plummet, in contrast, the number of rational supporters after the system is balanced reaches a high level, which is exactly what we expect.It can be concluded thatθ severely disturbs the number of users in the ODE. When θ is larger, more opponents will stop spreading negative information and turn into silent users. As a result, the proportion of supporters in this ecosystem increases continually, and ignorant users will have a greater probability of contacting supporters. Thus, more users begin to support the ODI and become internal supporters. To maintain the health of the ODE and promote its sustainable development, internal organizations or other stakeholders should pay close attention to the conversion trends of latent users, reduce the direct conversion of latent users into silent users, and make more users participate in the data activities. In addition, organizations also need to take effective measures to guide users. Then, they can create a positive atmosphere within the ecosystem space to put pressure on opponents. Additionally, they also need to establish appropriate rewards or punishments to increase the opponent-silent rate.


### 4.2.4. The Impact of the Reversal Rate

Figure16, 17 and 18 present the ODI rational supporters, irrational supporters, and opponents, respectively, under different reversal rates ξ, m, or n over time t. Overall, the interaction between the three has some impact on the structure of the ODE, but the reversal rate disturbs the number of rational and irrational supporters more severely, while the impact on the change in the number of opponents is not obvious.Figure 16
Number of rational supporters, irrational supporters, and opponents versus time varying over different rational reversal ratesξ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 17
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive reversal rates (m) withε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 18
Number of rational supporters, irrational supporters, and opponents versus time varying over different negative reversal rates (n) withε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)As the rational reversal rateξ increases, the number of rational supporters gradually increases, while the number of irrational supporters gradually decreases due to the transformation of irrational supporters to rational supporters. When ξ increased to a higher level (from 0.001 to 0.01), the number of rational and irrational supporters dropped sharply, while the fluctuations in the number of opponents were not as substantial as those of the supporters.As the positive reversal ratem increases, the numbers of both rational supporters and irrational supporters show a growing trend and remain at a high level after the system reaches equilibrium, while the number of opponents basically remains at a low level. Similarly, as the negative reversal rate n gradually decreases, the number of rational and irrational supporters also shows a considerable increasing trend, but the number of opponents is still at a low level. It is easy to understand that as m increases or n decreases, more opponents will become supporters (whether rational or irrational), which leads to a reduction in the exposure of ignorant users to negative information and a direct decrease in the total number of opponents.In response to the above simulation results, internal organizations and other stakeholders in the ODE should focus on how to convert ODI opponents. For example, official agencies can counter negative information by publishing authoritative information, and thus, more opponents can understand the actual policies and benefits of the ODI. The organization should also enhance data transparency to respond to the negative attitude of the opponents, thereby awakening the opponents to support the ODI.


## 4.2.1. The Impact of Users-Contacting Rate

Figure6 and 7 describe that the number of ODI rational supporters, irrational supporters, and opponents changes with different supporter contact rates over time t. In general, the larger the supporter contact rate is, the greater the number of users in the three groups, and they will reach the peak faster. However, there is a fact that should be mentioned. On the one hand, there is a greater increase in the supporter contact rate from 0.02 to 0.2. However, rational supporters and opponents will not change considerably when they reach a stable state. On the other hand, when the supporter contact rate increases, the number of opponents in the early period will rise, but the time to reach the peak and decline will be dramatically earlier.Figure 6
Number of rational supporters, irrational supporters, and opponents versus time-varying over different supporter contact ratesμ1 with ε = 1, ρ = 0.005, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 7
Number of rational supporters, irrational supporters, and opponents versus time varying over different supporter contact ratesμ2 with ε = 1, ρ = 0.005, μ1 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure8 depicts the number of rational supporters, irrational supporters, and opponents with different opponent contact rates φ. The changing trends of the three types under different φ are similar to the above changing trends. When the opponent contact rate decreases to a low level, such as 0.00002 to 0.000002, the number of supporters and opponents does not change substantially.Figure 8
Number of rational supporters, irrational supporters, and opponents versus time varying over different opponent contact ratesφ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)In summary, when users are in a high supporter contact rate area, more ignorant users would contact supporters and turn into latent users. This also leads to more latent users becoming opponents, causing the number of opponents to increase considerably. When there are users in a low opponent contact rate area, the number of opponents has no substantial decline, but the proportion of supporters decreases. Based on this, the internal organization of the ecosystem should control the correct development direction. If they only blindly use their power to control the user contact rate, it will not turn more ignorant users into supporters, but it will be counterproductive.


## 4.2.2. The Impact of the Users-Conversing Rate

Figure9, 10, and 11 demonstrate the number of ODI rational supporters, irrational supporters, and opponents over time t with different user conversion rates. Three interesting phenomena are discovered:Figure 9
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive-rational-conversing ratesα1 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 10
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive-irrational-conversing ratesα2 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 11
Number of rational supporters, irrational supporters, and opponents versus time varying over different negative-conversing ratesβ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)First, with the increase in the positive-rational-conversing rateα1, although the number of supporters is boosting, they are still maintained at a very low level after the system is balanced. Moreover, as the negative conversion rate β decreases, the number of opponents cannot be reduced, which is inconsistent with our common sense. Second, the number of rational supporters, irrational supporters, and opponents will increase due to the increase in the positive-irrational-conversing rate α2. However, the number of opponents has gradually increased after system stabilization, but its peak has been continuously decreasing. Third, with the decrease in β, the peak of the opponent group rapidly decreases, but the number of opponents in the balanced stage gradually increases. Meanwhile, the number of supporters changes very slightly after β is reduced to a certain level (0.0005 to 0.0001).One possible explanation is that as the negative-conversing rateβ decreases, although the number of latent users directly becoming opponents decreases, more latent users will turn into irrational supporters due to their “swing” characteristic, and then more irrational supporters will turn into opponents, which increases the number of opponents indirectly. The phenomenon caused by α1 is the same as the effect brought by β. In addition, this also explains why the numbers of the three groups will increase as α2 increases.Due to the above, organizations in the ODE need to take actions to increase publicity within a controllable range, and thus, more potential users can truly understand the true content of the ODI. Organizations can also use advanced technology to analyze the emotional tendencies and psychological attractiveness of users. They can also formulate and publish more targeted policies to make users truly trust the convenience and benefits brought by the ODE. In this way, the number of irrational supporters and opponents could be reduced.


## 4.2.3. The Impact of the Silent Rate

Figure12 illustrates the rational supporters, irrational supporters, and opponents under different latent-silent rates γ over time t. As the value of γ gradually increases, the number of rational supporters, irrational supporters, and opponents considerably drops, and its peak falls off a cliff. A larger value of γ means that more ignorant users skip the information diffusion stage, and they do not participate in any data activities in the ODE.Figure 12
Number of rational supporters, irrational supporters, and opponents versus time varying over different latent-silent ratesγ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure13, 14 and 15 describe the ODI rational supporters, irrational supporters, and opponents, respectively, under different silence rates over time t.Figure 13
Number of rational supporters, irrational supporters, and opponents versus time varying over different rational-silent ratδ1 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 14
Number of rational supporters, irrational supporters, and opponents versus time varying over different irrational silence ratesδ2 with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 15
Number of rational supporters, irrational supporters, and opponents versus time varying over different opposite-silence ratesθ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Observing Figures13 and 14, we can find that when the rational-silent rate δ1 increases, only the number of rational supporters decreases, and the number of irrational supporters and opponents does not show any substantial change. When the irrational-silent rate δ2 increases, the number of rational supporters and irrational supporters decreases, while the number of opponents still does not show any obvious changes.In Figure15, comparing the trend of the opponent-silent rate θ with δ1 and δ2, we can find that even a small fluctuation of θ would have a severe impact on rational supporters, irrational supporters, and opponents. The number of rational and irrational supporters increases with the continuous increase of θ, while the number of opponents decreases. Moreover, when θ increases from a lower level to a higher level, although the peak of opponents will plummet, in contrast, the number of rational supporters after the system is balanced reaches a high level, which is exactly what we expect.It can be concluded thatθ severely disturbs the number of users in the ODE. When θ is larger, more opponents will stop spreading negative information and turn into silent users. As a result, the proportion of supporters in this ecosystem increases continually, and ignorant users will have a greater probability of contacting supporters. Thus, more users begin to support the ODI and become internal supporters. To maintain the health of the ODE and promote its sustainable development, internal organizations or other stakeholders should pay close attention to the conversion trends of latent users, reduce the direct conversion of latent users into silent users, and make more users participate in the data activities. In addition, organizations also need to take effective measures to guide users. Then, they can create a positive atmosphere within the ecosystem space to put pressure on opponents. Additionally, they also need to establish appropriate rewards or punishments to increase the opponent-silent rate.


## 4.2.4. The Impact of the Reversal Rate

Figure16, 17 and 18 present the ODI rational supporters, irrational supporters, and opponents, respectively, under different reversal rates ξ, m, or n over time t. Overall, the interaction between the three has some impact on the structure of the ODE, but the reversal rate disturbs the number of rational and irrational supporters more severely, while the impact on the change in the number of opponents is not obvious.Figure 16
Number of rational supporters, irrational supporters, and opponents versus time varying over different rational reversal ratesξ with ε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, (m) = 0.0005, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 17
Number of rational supporters, irrational supporters, and opponents versus time varying over different positive reversal rates (m) withε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (n) = 0.003, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)Figure 18
Number of rational supporters, irrational supporters, and opponents versus time varying over different negative reversal rates (n) withε = 1, ρ = 0.005, μ1 = 0.0002, μ2 = 0.0002, φ = 0.0002, α1 = 0.005, α2 = 0.005, β = 0.01, θ = 0.05, δ1 = 0.003, δ2 = 0.003, ξ = 0.004, (m) = 0.0005, γ = 0.002. (a) S1(t), (b) S2(t), (c) O(t).
(a)(b)(c)As the rational reversal rateξ increases, the number of rational supporters gradually increases, while the number of irrational supporters gradually decreases due to the transformation of irrational supporters to rational supporters. When ξ increased to a higher level (from 0.001 to 0.01), the number of rational and irrational supporters dropped sharply, while the fluctuations in the number of opponents were not as substantial as those of the supporters.As the positive reversal ratem increases, the numbers of both rational supporters and irrational supporters show a growing trend and remain at a high level after the system reaches equilibrium, while the number of opponents basically remains at a low level. Similarly, as the negative reversal rate n gradually decreases, the number of rational and irrational supporters also shows a considerable increasing trend, but the number of opponents is still at a low level. It is easy to understand that as m increases or n decreases, more opponents will become supporters (whether rational or irrational), which leads to a reduction in the exposure of ignorant users to negative information and a direct decrease in the total number of opponents.In response to the above simulation results, internal organizations and other stakeholders in the ODE should focus on how to convert ODI opponents. For example, official agencies can counter negative information by publishing authoritative information, and thus, more opponents can understand the actual policies and benefits of the ODI. The organization should also enhance data transparency to respond to the negative attitude of the opponents, thereby awakening the opponents to support the ODI.


## 5. Conclusions

This research proposes an ILSOC information diffusion model to delineate the process of information diffusion and interaction among users within the ODE. This model contemplates the open characteristics of the ODE, adds population dynamics, and considers the swing behaviors of users to examine the influence of users on the sustainable development of the open data ecosystem. The simulation results show that eight parameters, the user contact rate (μ1, μ2, φ), negative conversion rate (β), latent-silent rate (γ), opponent-silent rate (θ), and reversal rate (m, n), will have some impact on the open data ecosystem. Therefore, organizations and stakeholders that manage the open data ecosystem can improve the structural relationships between users in the following ways to promote open data ecosystem sustainability:First, a balanced range of user contact rates (μ1, μ2, and φ) is maintained. The contact rates that become too higher or too lower both have an adverse impact on the open data ecosystem. In other words, information behavior between users cannot be improved simply by stimulating the users’ interactions. Second, the negative conversion rate β is controlled at a low level. A lower negative-conversing rate can help the number of internal supporters to be in a higher proportion, ensuring support from most internal users of the system for the ODI. Third, measures should be taken to reduce the latent-silent rate γ and increase the opponent-silent rate θ. A lower latent-silent rate can enable more latent users to participate in the data sharing process in the ecosystem, and a higher opponent-silent rate can turn more opponents into silent users, which can stop spreading negative information.Finally, the positive reversal ratem increases and the negative reversal rate n decreases. Controlling the reversal rate can capable more opponents to turn into supporters and reduce the probability of ignorant users encountering negative information. This research pays heed attention to the interactions between users affecting the sustainability of the open data ecosystem. However, with the “data governance” concept emerging in recent years, research about the open data ecosystem still has numerous issues that should be discussed. These issues include the amount of influence that will be made by the subjective assumptions and other user psychological factors to the open data ecosystem, the use of other models, such as fuzzy systems [34] for researching open data ecosystems, and the amount of factors that will affect the sustainable development of the open data ecosystem, as well as the priorities and correlations among them. We should proceed next from the existing research to explore some effective strategies and ensure the sustainable development of the open data ecosystem in the future.



---

*Source: 2892274-2022-04-15.xml*