TITLE:
Asymptotic Behavior and Stability of Stochastic SIR Model with Variable Diffusion Rates
AUTHORS:
Xianhua Xie, Li Ma, Jingfei Xu
KEYWORDS:
SIR Model, Regularity, Lyapunov Function, Stochastic Asymptotic Stability
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.8,
August
7,
2017
ABSTRACT: In this paper, we propose random fluctuation on contact and recovery rates in
deterministic SIR model with disease deaths in nonparametric manner and
derive a new stochastic SIR model with distributed time delay and general
diffusion coefficients. By analysis of the introduced model, we obtain the sufficient
conditions for the regularity, existence and uniqueness of a global solution
by means of Lyapunov function. Moreover, we also investigate the stochastic
asymptotic stability of disease free equilibria and endemic equilibria of
this model. Finally, we illustrate our general results by applications.