A Markovian regime-switching stochastic SEQIR epidemic model with governmental policy

TL;DR

A stochastic SEQIR epidemic model with Markovian regime-switching is proposed and investigated, and the existence and uniqueness of the globally positive solution to the stochastic model by using the Lyapunov method is found.

Abstract

In this paper, a stochastic SEQIR epidemic model with Markovian regime-switching is proposed and investigated. The governmental policy and implement efficiency are concerned by a generalized incidence function of the susceptible class. We have the existence and uniqueness of the globally positive solution to the stochastic model by using the Lyapunov method. In addition, we study the dynamical behaviors of the disease, and the sufficient conditions for the extinction and persistence in mean are obtained. Finally, numerical simulations are introduced to demonstrate the theoretical results.

Figures (5)

• Figure 1: Simulation of Markov chain $r(t)$ with $r(0)=3$.
• Figure 2: Simulations of $E(t),Q(t),I(t)$ with ${R}_0^*<1$.
• Figure 3: Simulations of $E(t),Q(t),I(t)$ with ${R}_0^*<1$ and $r(t)=1,2,3,4$.
• Figure 4: Simulations of $E(t),Q(t),I(t)$ with $\widetilde{R}_0^*>1$.
• Figure 5: Simulations of $E(t),Q(t),I(t)$ with $\widetilde{R}_0^*>1$ and $r(t)=1,2,3,4$.