Solution of epidemic models with quenched transients

被引:9
作者
Filipe, JAN [1 ]
Gilligan, CA [1 ]
机构
[1] Univ Cambridge, Dept Plant Sci, Cambridge CB2 3EA, England
来源
PHYSICAL REVIEW E | 2003年 / 67卷 / 02期
关键词
D O I
10.1103/PhysRevE.67.021906
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We consider a model for single-season disease epidemics, with a delay (latent period) in the onset of infectivity and a decay ("quenching") in host susceptibility described by time-varying rates of primary and secondary infections. The classical susceptible-exposed-infected (SEI) model of epidemiology is a special case with constant rates. The decaying rates force the epidemics to slow down, and eventually stop in a "quenched transient" state that depends on the full history of the epidemic including its initial state. This equilibrium state is neutrally stable (i.e., has zero-value eigenvalues), and cannot be studied using standard equilibrium analysis. We introduce a method that gives an approximate analytical solution for the quenched state. The method uses an interpolation between two exactly solvable limits and applies to the whole, five-dimensional parameter space of the model. Some applications of the solutions for analysis of epidemics are given.
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页数:8
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