Almarashi Reem M, McCluskey C Connell
Saudi Electronic University Jeddah, Jeddah, Saudi Arabia.
Wilfrid Laurier University Waterloo, ON, Canada.
J Math Biol. 2019 Aug;79(3):1015-1028. doi: 10.1007/s00285-019-01387-8. Epub 2019 May 24.
Many disease transmission models exhibit a threshold behaviour based on the basic reproduction number [Formula: see text], where the disease-free equilibrium is locally asymptotically stable if [Formula: see text] and unstable if [Formula: see text]. However, if a system includes immigration of infected individuals, then there is no disease-free equilibrium. We consider how the disease-free equilibrium moves as the level of immigration of infected individuals is increased from 0, finding, under mild assumptions, that the disease-free equilibrium becomes an endemic equilibrium if [Formula: see text] and leaves the biologically relevant space (by having at least one coordinate become negative) if [Formula: see text].
许多疾病传播模型基于基本再生数[公式：见正文]表现出阈值行为，即如果[公式：见正文]，无病平衡点是局部渐近稳定的，而如果[公式：见正文]，则是不稳定的。然而，如果一个系统包括受感染个体的迁入，那么就不存在无病平衡点。我们考虑随着受感染个体迁入水平从0增加，无病平衡点如何移动，发现在温和假设下，如果[公式：见正文]，无病平衡点会变成地方病平衡点，如果[公式：见正文]，则会离开生物学相关空间（通过至少有一个坐标变为负数）。
