Recent work has produced examples where models of the spread of infectious disease with immigration of infected hosts are shown to be globally asymptotically stable through the use of Lyapunov functions. In each case, the Lyapunov function was similar to a Lyapunov function that worked for the corresponding model without immigration of infected hosts.We distill the calculations from the individual examples into a general result, finding algebraic conditions under which the Lyapunov function for a model without immigration of infected hosts extends to be a valid Lyapunov function for the corresponding system with immigration of infected hosts.Finally, the method is applied to a multi-group $ SIR $ model.

中文翻译：

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Lyapunov可用于感染宿主迁移的疾病模型

最近的工作产生了一些例子，其中通过使用李雅普诺夫函数，传染病传播与感染宿主迁移的模型在全球范围内是渐近稳定的。在每种情况下，Lyapunov函数都类似于在不迁移受感染宿主的情况下适用于相应模型的Lyapunov函数。对于被感染主机的相应系统，感染主机的迁移扩展为有效的Lyapunov函数。最后，该方法应用于多组$ SIR $模型。