The global structure of a spatial model of infectious disease
The global structure of a spatial model of infectious disease
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DOI：
10.1098/rspa.2002.1080
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发表时间：
2003-06
期刊：
影响因子：
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通讯作者：
I. Beardmore;R. Beardmore
中科院分区：
文献类型：
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作者：
I. Beardmore;R. Beardmore
本文研究了一个考虑空间非均匀性的传染病SI模型，得到了一个有界区域上的反应-对流-扩散方程组。包括对流过程来解释社会互动，如通过人口倾向于聚集的焦点或巢穴的位置来建模。结果表明，以出生率为分岔参数时，该模型稳态解出现了垂直分岔，并由此衍生出一个全局次级分支，该分支在无穷远处分岔。随后，我们利用奇异摄动技术给出了沿该分支在大、小参数极限下的极限空间结构的描述。最后，对一些与生物学相关的案例进行了数值说明。
In this paper we study an SI model of infectious diseases that takes into account spatial inhomogeneities, resulting in a system of reaction–convection–diffusion equations on a bounded domain. The convection process is included to account for social interaction, as modelled by the location of a focal point or den where the population will tend to aggregate. We show that a vertical bifurcation of steady–state solutions occurs in this model when birth rate is taken as the bifurcation parameter, from which emanates a global secondary branch, which then bifurcates at infinity. Subsequently, we use singular perturbation techniques to give a description of the limiting spatial structure along this branch in large and small parameter limits. Finally, the results are illustrated numerically on some biologically relevant cases.