Permanence and extinction for the stochastic SIR epidemic model

[摘要] The aim of this paper is to study the stochastic SIR equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises. We derive a sufficient and almost necessary condition for the extinction and permanence for SIR epidemic system with multi noises {dS(t) = [a(1 )- b(1)S(t) - I(t) f(S(t), I(t))]dt + sigma S-1(t)dB(1)(t) - I(t)g(S(t), I(t))dB(3)(t), dI(t) = [-b(2)I(t) + I(t) f(S(t), I(t))]dt + sigma 2I(t)dB(2)(t) + I(t)g(S(t), I(t))dB(3)(t). Moreover, the rate of all convergences of the solution are also established. A number of numerical examples are given to illustrate our results. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] SIR model;Extinction;Permanence;Stationary distribution;Ergodicity