Hancock Penny A, Godfray H Charles J
Natural Environment Research Council Centre for Population Biology & Division of Biology, Imperial College London, Silwood Park Campus, Ascot, Berks, UK.
Malar J. 2007 Jul 30;6:98. doi: 10.1186/1475-2875-6-98.
A series of models of malaria-mosquito-human interactions using the Lumped Age-Class technique of Gurney & Nisbet are developed. The models explicitly include sub-adult mosquito dynamics and assume that population regulation occurs at the larval stage. A challenge for modelling mosquito dynamics in continuous time is that the insect has discrete life-history stages (egg, larva, pupa & adult), the sub-adult stages of relatively fixed duration, which are subject to very different demographic rates. The Lumped Age-Class technique provides a natural way to treat this type of population structure. The resulting model, phrased as a system of delay-differential equations, is only slightly harder to analyse than traditional ordinary differential equations and much easier than the alternative partial differential equation approach. The Lumped Age-Class technique also allows the natural treatment of the relatively fixed time delay between the mosquito ingesting Plasmodium and it becoming infective. Three models are developed to illustrate the application of this approach: one including just the mosquito dynamics, the second including Plasmodium but no human dynamics, and the third including the interaction of the malaria pathogen and the human population (though only in a simple classical Ross-Macdonald manner). A range of epidemiological quantities used in studying malaria such as the vectorial capacity, the entomological inoculation rate and the basic reproductive number (R0) are derived, and examples given of the analysis and simulation of model dynamics. Assumptions and extensions are discussed. It is suggested that this modelling framework may be a natural and useful tool for exploring a variety of issues in malaria-vector epidemiology, especially in circumstances where a dynamic representation of mosquito recruitment is required.
利用格尼和尼斯比特的集总年龄组技术，开发了一系列疟疾-蚊子-人类相互作用模型。这些模型明确纳入了亚成蚊动态，并假设种群调节发生在幼虫阶段。在连续时间内对蚊子动态进行建模面临的一个挑战是，这种昆虫具有离散的生活史阶段（卵、幼虫、蛹和成虫），亚成蚊阶段持续时间相对固定，且各阶段的人口统计学比率差异很大。集总年龄组技术提供了一种处理这类种群结构的自然方法。由此产生的模型表述为一个延迟微分方程组，其分析难度仅比传统常微分方程略高，远低于替代的偏微分方程方法。集总年龄组技术还允许自然处理蚊子摄入疟原虫到具有感染性之间相对固定的时间延迟。开发了三个模型来说明这种方法的应用：一个仅包括蚊子动态，第二个包括疟原虫但不包括人类动态，第三个包括疟疾病原体与人类种群的相互作用（尽管只是以简单的经典罗斯-麦克唐纳方式）。推导了一系列用于研究疟疾的流行病学指标，如媒介能量、昆虫接种率和基本繁殖数（R0），并给出了模型动态分析和模拟的示例。讨论了模型假设和扩展内容。建议该建模框架可能是探索疟疾媒介流行病学中各种问题的一种自然且有用的工具，特别是在需要动态表示蚊子繁殖的情况下。
