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

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 ).