具有垂直传染和分布时滞的SEI传染病模型

SEI Infectious Disease Model with Vertical Transmission and Distribution Time Delay

本文以北美僵尸鹿传染病传播特征为生物背景,建立了具有垂直传染和分布时滞的SEI传染病模型。通过定义界定疾病是否传播的基本再生数R0,分别给出了模型无病平衡点全局渐近稳定以及患病鹿群持久生存的充分条件:即当R0 ≤ 1时,无病平衡点E0是全局渐近稳定的;当R0 > 1时,患病鹿群是持久的。文末的数值模拟不仅验证了定性理论结果的正确性,同时展示了僵尸鹿病毒潜伏期和死亡率对鹿种群数量的影响。

In this paper, we study an SEI infectious disease model with vertical transmission and distribution time delay that was developed using the infectious disease transmission characteristics of zombie deer in North America as the biological background. By defining the basic reproduction number that defines whether the disease is transmitted or not, sufficient conditions are given for the global asymptotic stability of the disease-free equilibrium point and the persistence of the diseased deer population, respectively: when the basic reproduction number less than or equal to one, the dis-ease-free equilibrium point is globally asymptotically stable;when the basic reproduction number greater than one, the diseased deer population is persistent. The numerical simulation at the end of the paper not only verifies the correctness of the qualitative theoretical results, but also demon-strates the effects of zombie deer virus incubation period and mortality on deer population size.