Arino Julien, Davis Jonathan R, Hartley David, Jordan Richard, Miller Joy M, van den Driessche P
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4.
Math Med Biol. 2005 Jun;22(2):129-42. doi: 10.1093/imammb/dqi003. Epub 2005 Mar 18.
A model is formulated that describes the spatial propagation of a disease that can be transmitted between multiple species. The spatial component consists, for each species, of a certain number of patches that make up the vertices of a digraph, the arcs of which represent the movement of the various species between the patches. In each of the patches and for each species, a susceptible-exposed-infectious-recovered (SEIR) epidemic model describes the evolution of the disease status of individuals. Also in each patch, there is transmission of the disease from species to species. An analysis of the system is given, beginning with results on the mobility component. A formula is derived for the computation of the basic reproduction number R(0) for sspecies and npatches, which then determines the global stability properties of the disease free equilibrium. Simulations for the spread of a disease in one species and two patches are presented.
建立了一个模型，用于描述可在多个物种之间传播的疾病的空间传播。对于每个物种，空间部分由一定数量的斑块组成，这些斑块构成一个有向图的顶点，其弧表示不同物种在斑块之间的移动。在每个斑块中，对于每个物种，一个易感-暴露-感染-康复（SEIR）流行病模型描述了个体疾病状态的演变。同样在每个斑块中，存在疾病在物种之间的传播。给出了对该系统的分析，首先是关于移动性部分的结果。推导出了一个用于计算(s)个物种和(n)个斑块的基本再生数(R(0))的公式，该公式进而确定了无病平衡点的全局稳定性性质。给出了一种疾病在一个物种和两个斑块中传播的模拟。
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