A stochastic hybrid differential equation model: Analysis and application

Abstract

Infectious diseases represent a real challenge to humanity and a true challenge for researchers to propose relevant solutions in order to reduce the number of infected individuals. Mathematical modeling of infectious diseases represents a better way to understand and control the spread of epidemics. In this work, we propose a stochastic SIQS epidemic model with a nonlinear incidence function and Markov switching. Firstly, we present our proposed stochastic model and its parameters. Secondly, we show the global existence and uniqueness of the positive solution. Then, we show a sufficient condition for the extinction of disease. Finally, we give numerical simulation to enrich our analytical results.