Global properties of infectious disease models with nonlinear incidence
Global properties of infectious disease models with nonlinear incidence
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DOI：
10.1007/s11538-007-9196-y
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发表时间：
2007-08-01
影响因子：
3.5
通讯作者：
Korobeinikov, Andrei
中科院分区：
文献类型：
--
作者：
Korobeinikov, Andrei
我们考虑传染病的经典SIR、SIRS和SEIR模型的全局性质，包括具有垂直传播的模型，假设水平传播由未指定的函数f（S，I）控制。我们构造了Lyapunov函数，使我们能够找到足以保证全局渐近稳定平衡状态存在和唯一性的生物现实条件。这种状态可以是地方性的，也可以是无感染的，这取决于基本繁殖数的值。
We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission is governed by an unspecified function f(S,I). We construct Lyapunov functions which enable us to find biologically realistic conditions sufficient to ensure existence and uniqueness of a globally asymptotically stable equilibrium state. This state can be either endemic, or infection-free, depending on the value of the basic reproduction number.