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Acta Mathematica Vietnamica

Long-Time Behavior of a Stochastic SIQR Model with Markov Switching

Nguyen Huu Du , icon-email Nguyen Thanh Dieu , Tran Quan Ky , Vu Hai Sam

Abstract

In this paper, we consider a stochastic SIQR model with a perturbed disease transmission coefficient. We determine the threshold λ that is used to classify the extinction and permanence of the model. Concretely, λ<0 implies that the disease-free equilibrium K(0,0,0) is globally asymptotically stable; that is, the disease will disappear and the entire population will become susceptible individuals. If λ>0, the model is strongly stochastically permanent. Our findings are considered significant improvements over the results in Liu et al. (Appl. Math. Comput. 316, 310–325 2018).