一类流行性出血热模型的全局稳定性

Global stability of an epidemic hemorrhagic fever model

建立和分析了一类流行性出血热传播模型,定义了模型的基本再生数R0,并利用Routh-Hurwitz判据、Lyapunov函数、LaSalle不变集原理和合作系统理论,讨论了模型平衡点的局部和全局渐近稳定性.结果表明:当R0<1时,模型仅存在唯一的无病平衡点,且无病平衡点是全局渐近稳定的;当R0>1时,无病平衡点不稳定,模型还存在地方病平衡点,且地方病平衡点全局渐近稳定.

In this paper,an epidemic hemorrhagic fever model is formulated and investigated.The basic reproduction number R0 for the model is identified.Local and global stability of the equilibria is discussed by using the Routh-Hurwitz criterion,Lyapunov function and LaSalle invariant set principle,and the theory of cooperate systems.The results show that if R0<1,there is only a disease-free equilibrium,which is globally asymptotically stable;while if R0>1,the disease-free equilibrium is unstable,there also exists a unique endemic equilibrium,which is globally asymptotically stable.