Stability and asymptotic properties of the SEQIR epidemic model?

In this paper, we investigate the SEQIR epidemic model with governmental measures that include vaccine subsidy, complete or semi-lockdown, etc. We first obtain the globally asymptotic stability of the disease-free equilibrium and the endemic equilibrium of the deterministic model, respectively. Then we propose the stochastic model and prove the existence and uniqueness of the positive solution to it. Further, by constructing suitable Lyapunov functions we obtain the condition for the extinction of diseases, which implies that the large noise can make the disease die out exponentially. Moreover, the asymptotic properties of the solution to the stochastic model is obtained. Finally, we carry out numerical simulations to verify our results.(c) 2023 Elsevier Ltd. All rights reserved.