具非线性传染率染病年龄结构SIR流行病模型渐近分析

研究了一类具非线性传染率染病年龄结构SIR流行病传播的数学模型的动力学性态,得到了疾病绝灭和持续生存的阈值条件——基本再生数.当基本再生数小于或等于1时,仅存在无病平衡点,且在其小于1的情况下,无病平衡点全局渐近稳定,疾病将逐渐消除;当基本再生数大于1时,存在不稳定的无病平衡点和唯一的局部渐近稳定的地方病平衡点,疾病将持续存在.本文的结论包含了相应常微分方程模型已有的相关结论.

An Asymptotic Analysis of an Infection-Age-Dependent SIR Epidemic Model with Nonlinear Infectivity

The dynamical behavior of an infection-age-dependent SIR epidemic model with nonlinear infectivity is studied and the threshold, a basic reproductive number which determines the outcome of the infectious disease, is found. When the basic reproductive number is less than or equal to 1, there exists only the disease-free equilibrium. Moreover, when the basic reproductive number is less than 1, the disease-free equilibrium is globally asymptotically stable and the disease will die out, whereas, when the basic reproductive number is greater than 1, there exist both the disease-free equilibrium which is unstable and the endemic equilibrium which is locally asymptotically stable, and the disease will persist. The paper concludes with the relevant results of the corresponding ODE models.