AAM  >> Vol. 2 No. 2 (May 2013)

    The Global Stability of a SEIRS Epidemic Model

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王 霞:山西大学,太原;

SEIRS模型全局稳定性非线性发病率Lyapunov函数复合矩阵 SEIRS Model; Global Stability; Nonlinear Incidence; Lyapunov Function; Compound Matrix


本文主要研究的SEIRS传染病模型中的发病率是具有人为影响的一般非线性的,出生率和死亡率均为常数。基本再生数决定论疾病的稳定性和存在及灭亡。若R0 ≤ 1时,则无病平衡点存在且唯一,是全局渐进稳定的,此时疾病会灭亡。若R0 > 1,则存在唯一的地方性平衡点,且是全局渐进稳定的,此时疾病会一直持续下去形成地方病。

In this paper, a SEIRS epidemic model with generally nonlinear incidence rate, which can be influenced by psychological effect, and constant recruitment and disease-caused death in epidemiology is considered. It is investigated that the global dynamic is completely determined by the basic reproduction number . If holds, then the only disease-free equilibrium is global stable and the disease dies out. If holds, then the unique endemic equilibrium in its feasible region is globally stable and the disease persists at an endemic equilibrium state.

王霞, 洪凤玲, 闫卫平. 一类SEIRS传染病模型的全局稳定性[J]. 应用数学进展, 2013, 2(2): 83-88. http://dx.doi.org/10.12677/AAM.2013.22011


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