Effect of mutations on stochastic dynamics of infectious diseases, a probability approach

Abstract

We present a stochastic SIV model affected by random mutations. In addition to the stochastic structure of the model, the parameters and equilibria of the model are also stochastic processes. Therefore, the stability of the system changes randomly over time. Our goal is to provide a computational approach to system probabilities. Based on the stochastic behavior of the model, we give a definition to evaluate the success of the vaccination plan (Definition 3.3). In addition, we assess the chance of success by calculating model distributions, probabilities, and the mathematical expectation of the number of infected people (Theorem 3.6). Finally, we simulate the results to assess the likelihood of the extinction of COVID-19.