On the almost sure, and p-th moment exponential convergence and stochastic exponential stabilities for nonlinear stochastic epidemic models

Abstract

In this paper the almost sure exponential convergence and $p^{th}$ mean exponential convergence of a general nonlinear stochastic epidemic model are investigated. The stochastic epidemic model consists of Ito-stochastic differential equations with multiple-delays and general nonlinear incidence rate. The stochastic convergence and exponential stabilities of the epidemic model are examined and applied to find control measures for the disease. Moreover, the basic reproduction number for the disease is computed.