# Modeling and Analyzing Transmission of Infectious Diseases Using Generalized Stochastic Petri Nets
[30] proposed the Multiple information and Multiplex network-SIS (MM-SIS) model to explore the detailed processes and characteristics of multiple information in multiplex networks and used the Microscopic Markov Chain method to set dynamic equations. [PERSON] et al. [31] investigated dynamic characteristics of an SIS network epidemic model with Markovian switching. [PERSON] et al. [32] used the discrete-time Markov chain approach to study the spreading process of diseases with recurrent population mobility. [PERSON] et al. [33] proposed an epidemic risk assessment model based on 12 indicators by combining Markov chain and analytic hierarchy process (AHP). [PERSON] et al. [34] analyzed the epidemic situation of COVID-19 based on the epidemiological Markov model and studied the clinical risk factors of the patients based on the patient's cardinal data and clinical symptoms. [PERSON] et al. [35] proposed an epidemic model to investigate the interplay between disease spread and information diffusion on two-layered networks and built the dynamical equations for the epidemic dynamics by using the micro-Markov chain (MMC) method. In addition to using mathematical models to study the spread of infectious diseases, there are some researchers [36; 37; 38] that used the statistical phylogeography to track the spread of the highly pathogenic H5N1, HIV-1, and H9N2, and some researchers [39]used machine learning models to speculate on the transmission and evolution mechanism of COVID-19. The above methods of mathematical modeling or statistics are generally based on the epidemic data and then use the model to assess the development of the epidemic and predict the future trend; however, the ability to evaluate the epidemic prevention measures and countermeasures taken in the epidemic is insufficient. It is unable to analyze and evaluate the effect of epidemic prevention measures from the system-level understanding. Some infectious diseases have the characteristics of long incubation period, high infectivity during the incubation period, and carriers with mild or no symptoms which are more likely to cause negligence. Petri nets (PNs) originated from the dissertation of [PERSON] [40] in 1962 who proposed a powerful modeling formalism in computer science, system engineering, and many other disciplines. PNs combine a well-defined mathematical theory with a graphical representation of the dynamic behavior of systems which are suitable for representing and modeling the concurrent, asynchronous, distributed, or non-deterministic systems. PNs have been successfully applied to the biological systems [41; 42], biological networks [43; 44], the transmission of infectious diseases [45; 46], healthcare systems [47], etc. Therefore, in order to evaluate the effectiveness of epidemic prevention measures, we use Petri net to model and simulate the epidemic transmission process of infectious diseases such as COVID-19 from the management perspective, and analyze the effects of anti-epidemic measures. In this paper, the major contribution is that we propose a generalized stochastic Petri net (GSPN) framework to model and analyze the spread of infectious diseases. At first, the qualitative analyses are carried out for the infectious diseases transmission mode and the main factors affecting the virus transmission at different stages. Then, the GSPN framework is built to simulate the evolution process of the epidemic. Based on this framework's isomorphic Markov chain, we use the analysis techniques of Petri nets to calculate the probability of the steady state of each stage in the process of virus propagation, and analyze the equilibrium state of the system and its changing laws under different influencing factors. The rest of this paper is organized as follows. In Section 2, the definitions and notations of generalized stochastic Petri nets are briefly reviewed. In Section 3, we propose the general transmission model of infectious diseases based on the GSPN framework. The experimental analysis is given in Section 4. Finally, Section 5 summarizes the paper.