Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate

Abstract

In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold λ that is used to classify the extinction and permanence of the disease. In particular, λ < 0 implies that the disease-free (K, 0, 0) is globally asymptotic stable, i.e., the disease will eventually disappear. If λ > 0 the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in [10,11,16,20,21].

The threshold of a deterministic and a stochastic SIQS epidemic model with varying total population size

“… [39] solved the threshold of a stochastic SIR model. However, there existed few works on the thresholds of stochastic epidemic models, except [39] , [40] . That is, most studies just established the sufficient conditions of the extinction and persistence of the disease, and did not give the sufficient and necessary conditions.…”

Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

“…The stochastic switched model proposed by Han and Zhao in [7], when A = µ, α = 0 and the infection transmission process is modeled by the bilinear incidence rate (also called the incidence in mass action). The stochastic system addressed by Tuong et al [36], when A = Kµ (where K is a carrying capacity) and f (S, I, R) = f (S, I). The stochastic models presented in [33], when the switches between two or more regimes of environment are neglected and f (S, I, R) = f (S)g(I), and in [32], when the regime-switching is not considered.…”

Dynamics of a stochastic HIV/AIDS model with treatment under regime switching

“…The switching is often memoryless and the wait time for the next switching obeys an exponential distribution [44]. Owing to its theoretical and practical significance, epidemic models with regime switching have been paid much attention [29,23,50,47]. The external environment will affect people's body and mind [35].…”