Department of Applied Mathematics, Jilin University of Finance and Economics, Changchun, 130117, Jilin Province, P.R. China.
Department of Mathematics, Yanbian University, Yanji, 133002, Jilin Province, P.R. China.
Sci Rep. 2019 Jul 23;9(1):10696. doi: 10.1038/s41598-019-47131-6.
In this paper, we present a regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion. We utilize the Markov semigroup theory to obtain the existence of a unique stable stationary distribution. We prove that the densities of the distributions of the solutions can converge in L to an invariant density under certain condition. Moreover, the sufficient conditions for the extinction of the disease, which means the disease will die out with probability one, are given in two cases. Meanwhile, we obtain a threshold parameter which can be utilized in identifying the stochastic extinction and persistence of the disease. Some numerical simulations are given to illustrate the analytical results.
本文提出了一个具有比率相关发生率和退化扩散的开关 SIR 传染病模型。我们利用马尔可夫半群理论得到了唯一稳定的平稳分布的存在性。我们证明了在一定条件下，解的分布密度可以在 L 中收敛到一个不变密度。此外，在两种情况下给出了疾病灭绝的充分条件，这意味着疾病将以概率一消失。同时，我们得到了一个可以用来识别疾病随机灭绝和持续的阈值参数。给出了一些数值模拟来说明分析结果。
