Modeling Virus Dynamics by Colored Petri Nets: Ebola and COVID Case Study

In this paper, we propose and explore Petri nets as a uniform formal language for modeling viruses that includes modeling behavior patterns, virus dynamics and immune response at cellular level and tempo-spatial modeling of infection spreading through territories and population. We develop techniques to translate cellular automata models, both deterministic and stochastic, into colored Petri nets based on an example of known cellular automata for modeling and mimicking Ebola virus dynamics. This is a first step to extend the technique to study other infectious disease. The model scalability is provided by using software generators of Petri net models presented in early published papers together with formal technique for translating cellular automata with explicitly defined rules into infinite Petri nets. Cellular automata for Ebola virus dynamics use parametric specifications of rules that constitutes peculiarity of the present study together with technique for combining a few deterministic cellular automata into a stochastic cellular automata; the corresponding techniques have been developed in the present paper. The simulation results completely coincide with known results obtained via dedicated simulator. Having uniform language for models specification brings in advantages for models mutual transformations and adjusting parameters in complete accordance to known statistical information. To illustrate suitability of colored Petri net for modeling viruses based on behavioral patterns and SEIR approach, a model of COVID virus spreading over human population has been presented that was developed to formalize ideas behind CovidSIM simulator.