Modeling virus spread through interacting systems

In this work we show two different approaches to model virus spread in a large population of individuals: one is more theoretical whereas the second is numerical and relies on the theoretical background of Markov Chains. The first one consist in find a mean-field limit of the empirical measures of a system of interacting individuals. The individuals are represented by their position, viral load and immune system response and they follow a stochastic system. The second part of the thesis consist in numerical simulations of different versions of a cellular automaton built to model the COVID-19 epidemic. Giving different rules of interaction among the population we can build cellular automata with different complexity and realism. With the most realistic version we model the real case of infections in Pisa in a period of time that includes the lockdown. Moreover, we use our model even to find information about the incubation period, the serial interval and reproductive number