A study of stochastic epidemic model driven by liouville fractional brownian motion coupled with seasonal air pollution

Abstract

Air pollution can cause and provoke respiratory diseases. It is an important topic to the public, particularly in developing countries. Since there are many uncertain factors in the environment, stochastic differential equation model is a powerful tool to study the changes of air pollution and the transmission of infectious diseases. The removal of air pollutants as well as the transmission of diseases can be influenced by random perturbations with memories. In this research, we develop a mathematical model in the form of a system of stochastic differential equations driven by fractional Brownian motion of Liouville-type, coupled with seasonal air pollution, to study the dynamics of infectious respiratory disease spread. As a result , by using stochastic calculus techniques, we derive the equation for the level of air pollution.