Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations
Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations
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DOI：
10.1137/0152030
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发表时间：
1992-04
影响因子：
1.9
通讯作者：
C. Simon;J. Jacquez
中科院分区：
文献类型：
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作者：
C. Simon;J. Jacquez
异质种群的确定性流行病模型的一个重要课题是寻找平衡点的局部稳定性和全局稳定性条件，以及这些稳定性条件与流行病起飞阈值、流行病流行阈值和基本再生数之间的关系。迄今为止，大部分工作都是关于恒定大小的同质种群模型。出于对人类免疫缺陷病毒/获得性免疫缺陷综合征（HIV/AIDS）动力学模型的分析，作者对具有多个阶段的疾病的SI模型进行了该项目，这些疾病可能导致死亡，并且感染具有复杂混合模式和不同大小的异质人群。在这类模型中，甚至很难找到稳定阈值和再生数的解析表达式。作者展示了如何通过感染者传播疾病的接触次数可以用作李雅普诺夫函数来进行系统稳定性分析。
A major project in deterministic epidemiological modeling of heterogeneous populations is to find conditions for the local and global stability of the equilibria and to work out the relations among these stability conditions, the thresholds for epidemic take-off and endemicity, and the basic reproduction number(s). Most of the work to date has been on models of homogeneous populations of constant size. Motivated by their analysis of models of the dynamics of human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS), the authors carry out this project for SI models of diseases that have multiple stages, which can lead to death, and which infect heterogeneous populations with intricate mixing patterns and varying sizes. In such models, it is even difficult to find the analytical expression for the stability threshold and the reproduction number. The authors show how the number of disease-transmitting contacts by infectives can be used as a Lyapunov function to carry out a systematic stabili...