Yakowitz S, Blount M, Gani J
University of Arizona, Tucson 85721, USA.
IMA J Math Appl Med Biol. 1996 Dec;13(4):223-44.
The customary models for the AIDS epidemic are compartmentalized according to criteria such as risk factors, sexual habits, gender, race, age, and HIV status and stage. Hitherto, with very few exceptions, investigators have resorted to deterministic approximations or to simulation for the computational investigation of such models, which do not yield to purely analytic methods. The present paper describes a numerical technique, not dependent on Monte Carlo simulations, for such compartmentalized Markov population processes. Analytic error bounds and computational evidence suggest that this technique is quite accurate. The study is motivated and illustrated by a model for a prison system, with ten interrelated prisons, twenty compartments, and thousands of individuals. This model is of increasing interest in itself because the HIV/AIDS epidemic is particularly virulent among prison populations, where the environment offers special opportunities to investigate various prevention and educational programmes quantitatively. Our computational techniques are shown to be effective for the analysis of such a prison system, even though the resulting Markov process is an order of magnitude more complicated than other stochastic epidemic models currently being investigated. The modelling approach and numerical device appear to be applicable to a wide variety of population processes involving migration between population patches.
艾滋病流行的传统模型是根据风险因素、性行为习惯、性别、种族、年龄以及艾滋病毒感染状况和阶段等标准进行划分的。迄今为止，除了极少数例外情况，研究人员在对这类模型进行计算研究时，都采用确定性近似法或模拟法，因为这些模型无法采用纯粹的解析方法。本文描述了一种不依赖蒙特卡罗模拟的数值技术，用于此类划分的马尔可夫种群过程。解析误差界限和计算证据表明，该技术相当精确。本研究以一个监狱系统模型为动机并进行说明，该模型有十个相互关联的监狱、二十个分区以及数千名个体。这个模型本身越来越受关注，因为艾滋病毒/艾滋病在监狱人群中传播尤为严重，在这种环境下，有特殊机会对各种预防和教育项目进行定量研究。我们的计算技术被证明对分析这样一个监狱系统是有效的，尽管由此产生的马尔可夫过程比目前正在研究的其他随机流行病模型复杂一个数量级。这种建模方法和数值手段似乎适用于涉及种群斑块间迁移的各种种群过程。
