一类非线性染病年龄结构模型渐近性态

研究一类具有非线性染病年龄结构SIS流行病传播数学模型动力学性态,得到疾病绝灭和持续生存的阈值--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.

Asymptotic behavior of a nonlinear infection-age-dependent epidemic model

Dynamical behavior of a nonlinear infection-age-dependent SIS epidemic model is studied and the threshold, a basic reproductive number which determines the outcome of the infectious disease is founded. When the basic reproductive number is not greater than 1 meaning the disease will die out, there exists only a disease free equilibrium which is globally asymptotically stable except that the basic reproductive number equals 1. When the basic reproductive number is greater than 1 meaning the disease will persist, there are two equilibria, the disease free equilibrium which is unstable and the endemic equilibrium which is locally asymptotically stable.