一种艾滋病毒传播模型的定性分析。

Qualitative analysis of an HIV transmission model.

作者信息

Lin X

机构信息

Department of Mathematics, University of Alberta, Edmonton, Canada.

出版信息

Math Biosci. 1991 Apr;104(1):111-34. doi: 10.1016/0025-5564(91)90033-f.

DOI:10.1016/0025-5564(91)90033-f

PMID:1804451

Abstract

In 1988, a multiple-group model for HIV transmission with preferred mixing was proposed by Jacquez and coworkers. In the present paper, the work done by Jacquez et al. is extended. It is shown that the stability modulus of the Jacobian matrix at the no-disease equilibrium is a threshold for this model. Furthermore, if the no-disease equilibrium is unstable, the number of infected individuals will remain above a certain positive level regardless of initial levels; that is, the disease will persist uniformly. The stability of the endemic equilibrium in the case of restricted mixing is also studied. A series of sufficient conditions for local and global asymptotic stability of the endemic equilibrium are stated.

摘要

1988年，雅克兹及其同事提出了一种具有优先混合的HIV传播多组模型。在本文中，雅克兹等人所做的工作得到了扩展。结果表明，无病平衡点处雅可比矩阵的稳定性模量是该模型的一个阈值。此外，如果无病平衡点不稳定，无论初始水平如何，感染个体的数量将保持在某个正水平之上；也就是说，疾病将持续存在。本文还研究了有限混合情况下地方病平衡点的稳定性。给出了地方病平衡点局部和全局渐近稳定的一系列充分条件。