Stability Analysis of the Stochastic SIR Model with Discrete Delay

Abstract

The purpose of this paper is to propose the stochastic infectious model with time delay and to study the stability of the disease-free steady state. In the prevalence of infectious diseases, environmental change and individual difference cause some kinds of random fluctuations in the infection recovery rate, immune effect, etc. Hence, the stochastic infectious model plays an important role in the analysis of the infection disease. Moreover, in the vector-borne diseases such as malaria and dengue fever, there exists time delay caused by an incubation period in the virus development in the vectors (mosquitoes) on the transmission of disease. Taking these facts into consideration, we propose a stochastic SIR(susceptible-infected-recovered) model with time delay. We analyze stability of the disease-free steady state, and study the influence of time delay and the random noise on the stability by numerical simulations.