具有预防接种免疫力的双线性传染率SIR流行病模型全局稳定性

研究一类具有预防接种免疫力的双线性传染率 SIR流行病模型全局稳定性 ,找到了决定疾病灭绝和持续生存的阈值——基本再生数 R0 .当 R0 ≤ 1时 ,仅存在无病平衡态 E0 ;当 R0 >1时 ,存在唯一的地方病平衡态 E* 和无病平衡态 E0 .利用 Hurwitz判据及 Liapunov-Lasalle不变集原理可以得知 :当 R0 <1时 ,无病平衡态 E0 全局渐近稳定 ;当 R0 >1时 ,地方病平衡态 E*全局渐近稳定 ,无病平衡态 E0 不稳定 ;当 R0 =1时 ,计算机数值模拟结果显示 ,无病平衡态 E0 有可能是稳定的

Global Stability of SIR Epidemiologicai Model with Vaccinal Immunity and Bilinear Incidence Rates

The global stability of SIR epidemiological model with vaccinal immunty and bilinear incidence rates is (studied). The basic reproductive number R_0 is found, which determines the existence of the infective disease. When R_0≤1, there only exists disease free (equilibrium) E_0. While R_0>1, two equilibriums, the endemic equilibria E~* and the disease free (equilibrium) E_0 exist. By Hurwitz criterion and Liapunov-Lasalle invarient theorem, we have proved the disease free (equilibrium) E_0 is globally asymptotically stable if R_0<1, while the disease free equilibrium E_0 is unstable and the endemic (equilibrium) E~* is globally asymptotically stable if R_0>1. Specially, if the basic reproductive number R_0=1, the computer numerical value simulation implies the disease free equilibrium E_0 is possiblly stable.