Asymptotic behavior of a regime-switching SIR epidemic model with degenerate diffusion

Abstract

In this paper, we consider a stochastic SIR epidemic model with regime switching. The Markov semigroup theory will be employed to obtain the existence of a unique stable stationary distribution. We prove that, if R s < 0, the disease becomes extinct exponentially; whereas if R s > 0 and β(i) > α(i)(ε(i) + γ (i)), i ∈ S, the densities of the distributions of the solution can converge in L 1 to an invariant density.

A stochastic differential equation SIS model on network under Markovian switching

“…Regime-switching diffusions provide a more realistic description for many field of application, including epidemiology and population dynamics. [9,31,11,16,28,13,15,5]. However, for the best of our knowledge, there are not yet hybrid diffusion epidemic models that consider a network structured population.…”

Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems

“…Indeed, stochastic models could be more appropriate way of modeling in comparison with their deterministic counterparts, since they can provide some additional degree of realism. By introducing (stochastic) environmental noise, many investigators have studied stochastic epidemic models [14][15][16][17][18][19][20][21][22][23] and stochastic population models [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. ey focus on the e ect of environmental uctuations on the dynamic behavior of these models.…”

A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

“…The telegraph noise (namely, color noise) can be illustrated as a switching between two or more regimes of environment, which differ by factors such as nutrition or as rain falls [41] . Frequently, the switching among different environments is memoryless and the waiting time for the next switch is exponentially distributed [42,[44][45][46][47][48][49][50][51][52][53] . Thus we can model the regime switching by a continuous-time Markov chain with values in a finite state space, which drives the changes of the main parameters of epidemic models with state switchings of the Markov chain.…”