The onset of oscillatory dynamics in models of multiple disease strains
The onset of oscillatory dynamics in models of multiple disease strains
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DOI：
10.1007/s00285-002-0163-9
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发表时间：
2002-12-01
影响因子：
1.9
通讯作者：
Gog, JR
中科院分区：
文献类型：
--
作者：
Dawes, JHP;Gog, JR
我们研究了一个广义SIR模型的感染动力学的四个竞争的疾病菌株。该模型包含四个以前研究过的模型作为特例。不同的菌株通过交叉免疫机制间接相互作用;宿主群体中的个体可能对特定菌株的感染产生免疫力，即使他们只感染了不同但密切相关的菌株。几种不同的交叉免疫模型进行了比较，在死亡率远小于从感染中恢复的速度的极限。在这个极限下，模型的动力学的渐近分析是可能的。我们能够计算的Takens-Bogdanov分岔的位置和性质与存在的振荡动力学观察到以前的作者。
We examine a generalised SIR model for the infection dynamics of four competing disease strains. This model contains four previously-studied models as special cases. The different strains interact indirectly by the mechanism of cross-immunity; individuals in the host population may become immune to infection by a particular strain even if they have only been infected with different but closely related strains. Several different models of cross-immunity are compared in the limit where the death rate is much smaller than the rate of recovery from infection. In this limit an asymptotic analysis of the dynamics of the models is possible. and we are able to compute the location and nature of the Takens-Bogdanov bifurcation associated with the presence of oscillatory dynamics observed by previous authors.