Simple Models for the Transmission of Microparasites Between Host Populations Living on Noncoincident Spatial Domains
Simple Models for the Transmission of Microparasites Between Host Populations Living on Noncoincident Spatial Domains
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DOI：
10.1007/978-3-540-78273-5_3
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
W. Fitzgibbon;M. Langlais
中科院分区：
文献类型：
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作者：
W. Fitzgibbon;M. Langlais
本章的目的是提供一个简单的数学方法来模拟两个不同的空间域上生活的宿主种群之间的微寄生虫的传播。我们将考虑两种典型情况：（1）病媒传播的疾病;（2）环境传播的疾病。在我们的模型中，从一个种群的传染性个体到另一个种群的易感个体的直接水平交叉传播不会发生。相反，寄生虫的传播要么是通过传染病媒和易感个体之间的间接交叉接触（在情况（1）中，反之亦然），要么是通过易感宿主和环境污染部分之间的间接接触（在情况（2）中，反之亦然）。我们还将假设微寄生虫在其中一个宿主种群中是良性的，也就是说，它对个体的人口统计学和扩散没有影响。接下来我们假设它对第二个种群是致命的。在应用中，我们考虑的第二个种群是人类，而第一个种群是动物-鸟类或啮齿动物-种群。简单的数学确定性模型与时空异质性的发展，从基本系统的常微分方程的非结构化人口的反应扩散模型的空间结构化人口处理异质环境和人口生活在不同的栖息地。除了证明所得到的数学问题是适定的，我们还分析了地方病状态的存在性和稳定性。在某些情况下，给出了持久性阈值。
The goal of this chapter is to provide a simple mathematical approach to modeling the transmission of microparasites between two host populations living on distinct spatial domains. We shall consider two prototypical situations (1), a vector borne disease and, (2), an environmentally transmitted disease. In our models direct horizontal criss-cross transmission from infectious individuals of one population to susceptibles of the other one does not occur. Instead parasite transmission takes place either through indirect criss-cross contacts between infective vectors and susceptible individuals and vice-versa in case (1), and through indirect contacts between susceptible hosts and the contaminated part of the environment and vice-versa in case (2). We shall also assume the microparasite is benign in one of the host populations, a reservoir, that is it has no impact on demography and dispersal of individuals. Next we assume it is lethal to the second population. In applications we have in mind the second population is human while the first one is an animal – avian or rodent – population. Simple mathematical deterministic models with spatio-temporal heterogeneities are developed, ranging from basic systems of ODEs for unstructured populations to Reaction-Diffusion models for spatially structured populations to handle heterogeneous environments and populations living in distinct habitats. Besides showing the resulting mathematical problems are well-posed we analyze the existence and stability of endemic states. Under some circumstances, persistence thresholds are given.