Tan W Y, Xiang Z
Department of Mathematical Sciences, University of Memphis, TN 38152, USA.
Math Biosci. 1998 Aug 15;152(1):29-61. doi: 10.1016/s0025-5564(98)10013-5.
In this paper we have developed a state space model for the HIV epidemic in homosexual populations which have been divided into subpopulations according to sexual activity levels. In this model, the stochastic dynamic system model is the stochastic model of the HIV epidemic in terms of the chain multinomial model whereas the observation model is a statistical model based on the observed AIDS incidences. This model is applied to the San Francisco homosexual population for estimating the numbers of susceptible people, infective people and AIDS cases and for estimating the probabilities of HIV transmission from infective people to susceptible people given sexual contacts. The results show that the estimated numbers of AIDS incidence trace closely the observed numbers indicating the usefulness of the model. It is observed that the estimated numbers of latent people show multimodal curves and that HIV infection takes place during the primary stage and very late stage. The results have further shown that there are significant differences between the observed AIDS incidences and the estimates by the embedded deterministic model. These results indicate that using the embedded deterministic model to estimate the HIV-infected people and to predict future AIDS cases can be very misleading in some cases.
在本文中，我们针对同性恋人群中的艾滋病毒流行情况开发了一种状态空间模型，这些人群已根据性活动水平被划分为亚人群。在该模型中，随机动态系统模型是基于链式多项模型的艾滋病毒流行随机模型，而观测模型是基于观察到的艾滋病发病率的统计模型。此模型应用于旧金山同性恋人群，用于估计易感人群、感染人群和艾滋病病例的数量，以及估计在有性接触的情况下艾滋病毒从感染人群传播到易感人群的概率。结果表明，估计的艾滋病发病率与观察到的数字紧密吻合，表明该模型是有用的。据观察，估计的潜伏人群数量呈现多峰曲线，且艾滋病毒感染发生在初期阶段和非常晚期。结果还进一步表明，观察到的艾滋病发病率与嵌入式确定性模型的估计值之间存在显著差异。这些结果表明，在某些情况下，使用嵌入式确定性模型来估计艾滋病毒感染者和预测未来艾滋病病例可能会产生很大的误导。
