Korobeinikov Andrei
MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
Bull Math Biol. 2009 Jan;71(1):75-83. doi: 10.1007/s11538-008-9352-z. Epub 2008 Sep 4.
We consider global properties of compartment SIR and SEIR models of infectious diseases, where there are several parallel infective stages. For instance, such a situation may arise if a fraction of the infected are detected and treated, while the rest of the infected remains undetected and untreated. We assume that the horizontal transmission is governed by the standard bilinear incidence rate. The direct Lyapunov method enables us to prove that the considered models are globally stable: There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction number R0, this state can be either endemic (R0>1), or infection-free (R0< or =1).
我们考虑传染病的SIR和SEIR compartment模型的全局性质，其中存在几个并行的感染阶段。例如，如果一部分感染者被检测并治疗，而其余感染者未被检测和治疗，就可能出现这种情况。我们假设水平传播由标准双线性发病率控制。直接李雅普诺夫方法使我们能够证明所考虑的模型是全局稳定的：总是存在一个全局渐近稳定的平衡状态。根据基本再生数R0的值，这个状态可以是地方病状态（R0>1），或者是无感染状态（R0≤1）。
