Busenberg S, Cooke K, Hsieh Y H
Mathematics Department, Harvey Mudd College, Claremont, California, USA.
Math Biosci. 1995 Jul-Aug;128(1-2):185-210. doi: 10.1016/0025-5564(94)00072-8.
A model is proposed in which the spread of HIV/AIDS in the community is mainly due to the sexual interaction between a core group of female prostitutes and young unmarried males. Several threshold parameters are obtained that determine persistence of endemic proportions, persistence of total population, and the persistence of infective population given the extinction of endemic proportions in a population tending to infinity. Conditions are given for the existence of multiple endemic equilibria as well as the existence of multiple stable equilibria with separatrix and their asymptotic behavior and biological significance are discussed. In all cases, global analysis is accompanied by bifurcation diagrams, and numerical examples are provided for some particular cases of interest. This model was proposed with the recent rapid growth of the HIV/AIDS epidemic in Asia in mind.
提出了一个模型，其中社区中艾滋病毒/艾滋病的传播主要归因于核心女性性工作者群体与年轻未婚男性之间的性互动。得到了几个阈值参数，这些参数决定了地方病比例的持续性、总人口的持续性以及在人口趋于无穷大时地方病比例灭绝情况下感染人群的持续性。给出了多重地方病平衡点存在的条件，讨论了具有分界线的多重稳定平衡点的存在性及其渐近行为和生物学意义。在所有情况下，全局分析都伴随着分岔图，并针对一些感兴趣的特殊情况提供了数值示例。该模型是考虑到近期亚洲艾滋病毒/艾滋病疫情的快速增长而提出的。
