Simulation of COVID-19 epidemic spread using Stochastic Differential Equations with Jump diffusion for SIR Model

Mathematical epidemiology is one of the most important research areas, it has contributed to understanding the behavior and the impact also the prediction of infectious disease. One of the fundamental methods intended to see the behavior of the pandemic is the susceptible-infectious-recovered epidemic model. However, the deterministic approach of this model has some limitations in mathematical modeling, for that we propose to add a stochastic variation in SIR equations. In this paper we present a stochastic differential equation with jump-diffusion formula for COVID-19, then we estimate the parameters of our stochastic susceptible-infected-recovered model. Finally, we compare our result with real covid19 spread in Morocco.