A stochastic threshold for an epidemic model with isolation and a non linear incidence

Abstract

In this paper, we study a stochastic epidemic model with isolation and nonlinear incidence. In particular, we propose a stochastic threshold for the model without any sharp sufficient assumptions on model parameters as compared to existing works. Firstly, we establish the uniqueness of the global positive solution according to Lyapunov function method. Secondly, we prove stochastic permanence of the solutions. Then, we establish sufficient condition for the extinction. Thirdly, we investigate necessary and sufficient conditions for persistence in mean of the disease. Finally, we provide some numerical simulations to illustrate our theoretical results.

Understanding death risks of Covid-19 under media awareness strategy: a stochastic approach

“…Likewise, similar to the proof found in the study ran by [ 3 ], we have obtained the following result which proves the desired assertion and hence the theorem 3 . …”

Dynamical behavior of a stochastic SIQS model via isolation with regime-switching

“…Two important measures to reduce the infection rate are vaccination and isolation(or quarantine) [ 4 , 7 – 10 ]. Due to economic level, cultural concept and other reasons, the vaccination rate is sometimes not high in some regions, and isolation is one of the economic, practical and effective measures to control the spread of the disease.…”

Dynamical behavior of a higher order stochastically perturbed SIRI epidemic model with relapse and media coverage

“…Recently, stochastic differential equation models [17] , [18] , [19] , [20] , [21] , [22] have played an important role in various branches of applied sciences including infection dynamics and population dynamics, since they can provide some additional degree of realism compared to their deterministic counterparts [23] . And it is hence interesting to introduce the stochastic perturbation into the deterministic system to reveal the effect of environmental white noise on human disease [18] , [21] , [24] , [25] , [26] , [27] . For example, Gray et al.…”

“…The authors used the Markov semigroup theory to obtain the existence of a stable stationary distribution. Caraballo [27] analyzed a stochastic epidemic model with isolation and nonlinear incidence. They established sufficient condition for extinction and obtained necessary and sufficient conditions for persistence in mean of the disease.…”

“…However, in the literatures [18] , [21] and [27] , the authors didn’t consider the effect of the media coverage. In addition, in the literatures [18] and [21] , the diffusion matrix is degenerate, the authors cannot use the Has’minskii’s theory to obtain the ergodicity of a stationary distribution, while in the literature [27] , although the diffusion matrix is nondegenerate, the authors didn’t studied the existence and uniqueness of an ergodic stationary distribution which implies stochastic weak stability. Accordingly, it is necessary for us to consider both of them together.…”