Dynamical behavior of a stochastic sir epidemic model with general incidence function and immigration: case of COVID-19

Abstract

In this study, a novel stochastic model for coronavirus disease 2019 (COVID-19) transmission is formulated with the presence of immigration, vaccination and general incidence function. The environment variability in this work is characterized by Gaussian white noise. We prove the existence, uniqueness and positivity of the solution of the model and investigate the stochastic ultimate boundedness. Sufficient conditions are presented for the extinction of the disease according to the values of the threshold parameter R^S₀ that represents the basic reproduction number of our stochastic model. Moreover, we prove that the number of infected individuals is always persistent in the mean. Also, the sensitivity analysis is used to discover parameters that have impact on the threshold parameter R^S₀. Some numerical experiments are also presented to illustrate the theoretical results.