# A New Individual-Based Model to Simulate Malware Propagation in Wireless Sensor Networks
## 2 Related work  
The proposed mathematical models to study the propagation of malware in WSN can be global or individual models. In this section, a brief description has been made of both proposed models. Moreover, these models have been classified based on the compartmental, the type of model (e.g., continuous or discrete, deterministic or stochastic) and the mathematical tool used (for example: systems of partial differential equations (PDE), ordinary differential equation (ODE), cellular automata (CA) and Markov chain). Recently, several global models have been proposed to model malware spreading in WSN (see Reference [20] and references therein). For example, the authors in Reference [21] have described a SIR model including a discrete delay to effectively predict both the temporal dynamic behaviour and the spatial distribution of malware propagation in mobile WSN. That proposal is a global, continuous and deterministic model that has used PDE. An improved SIRS model was proposed in Reference [22], to characterise the process of worm propagation with the energy consumption and different distributed density of nodes. This model is based on a ODE. Also, it is a global, continuous and deterministic model. In Reference [23] the authors proposed a heterogeneous discrete-time SIS model. They predict the infection behaviour of malware by developing a non-cooperative non-zero-sum game to describe interactions between a heterogeneous WSN system and malware. This model is based on a Markov chain. Thus, it is a global, discrete and stochastic model. The authors of Reference [8] have studied the spread of malware on WANETs. The objective of this work has been to identify the propagation rate through two malware propagation schemes (unicast and broadcast) and two different network modes (spread and communication), based on the classic SI epidemic propagation model. It is a global, discrete and deterministic model, which has used ODE. The SIRD model proposed in Reference [9] has evaluated malware propagation on the narrowband Internet of Things based heterogeneous wireless sensor networks (NBIOT-HWSNs). The availability of nodes based on the distribution of heterogeneous nodes and vulnerabilities has been analyzed. This model has used the Markov chains, and it is a global, discrete and stochastic model. The authors of Reference [24] have proposed a novel IoT-SIS botnet propagation model based on IoT sensor networks. The impact of device power consumption and network density versus different botnet scanning methods has been analyzed. This model used ODE. Also, it is a global, discrete and deterministic model. A heterogeneous susceptible-insidious-infectious-recovered-dysfunctional (SNIRD) model on WSN has been proposed in Reference [25]. This model has included the \(N\) state for those infected sensors that have not been detected by the intrusion detection system (IDS), and the \(D\) state refers to nodes that have stopped functioning due to malware destruction, power exhaustion, or physical damage. This model has used the PDE, and it is a global, discrete and stochastic model. Subsequently, the specific characteristics of these networks have been taken into account in individual models like the following--in Reference [26] authors proposed a model that follows the state transition scheme of a typical SI infection model, but can microscopically compute the prior probability of each sensor being infected by the worm using several iterative equations of individual security states. This research is an individual, discrete and stochastic model that is based on a Markov chain. The authors of Reference [19] proposed an improved individual-based model that use particular features of three types of nodes and complex topology. The compartments of the model are susceptible, infected, recovered, damaged, and out-of-order. In this model, cellular automata are used. Furthermore, it is an individual, discrete and deterministic model.