Global analysis of multi-strains SIS, SIR and MSIR epidemic models
Global analysis of multi-strains SIS, SIR and MSIR epidemic models
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DOI：
10.1007/s12190-013-0693-x
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发表时间：
2014-02-01
影响因子：
2.2
通讯作者：
Sallet, G.
中科院分区：
文献类型：
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作者：
Bichara, D.;Iggidr, A.;Sallet, G.
考虑了具有标准质量作用和变化种群的SIS、SIR和MSIR模型，其中传染病的病原体为n种不同的菌株。我们还考虑了具有垂直传播的相同模型。我们证明了在一般条件下的竞争排斥原理。每一个品系都有一个基本的繁殖率。它对应于只有这种应变存在的情况。完整系统的基本再生产率是每个个体的基本再生产率的最大值。实际上，我们还为每个应变定义了一个等效阈值。竞争的赢家是具有最大阈值的菌株。事实证明，这种菌株是最致命的，即，这是地方病平衡为易感宿主种群提供最小种群的菌株。这可以被解释为一个pessimization原则。
We consider SIS, SIR and MSIR models with standard mass action and varying population, with n different pathogen strains of an infectious disease. We also consider the same models with vertical transmission. We prove that under generic conditions a competitive exclusion principle holds. To each strain a basic reproduction ratio can be associated. It corresponds to the case where only this strain exists. The basic reproduction ratio of the complete system is the maximum of each individual basic reproduction ratio. Actually we also define an equivalent threshold for each strain. The winner of the competition is the strain with the maximum threshold. It turns out that this strain is the most virulent, i.e., this is the strain for which the endemic equilibrium gives the minimum population for the susceptible host population. This can be interpreted as a pessimization principle.