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Long-Time Behavior of a Stochastic SIQR Model with Markov Switching
Nguyen Huu Du
,
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 $\lambda$ that is used to classify the extinction and permanence of the model. Concretely, $\lambda < 0$ 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 $\lambda > 0$, 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).