Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes

被引:37
作者
Ball, F
Britton, T
Lyne, O
机构
[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England
[2] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden
基金
英国工程与自然科学研究理事会;
关键词
stochastic epidemic; multitype household epidemic; threshold parameter; estimation; optimal vaccination scheme; critical vaccination coverage; linear programming;
D O I
10.1016/j.mbs.2004.05.001
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
This paper treats a stochastic model for an SIR (susceptible --> infective --> removed) multitype household epidemic. The community is assumed to be closed, individuals are of different types and each individual belongs to a household. Previously obtained probabilistic and inferential results for the model are used to derive the optimal vaccination scheme. By this is meant the scheme that vaccinates the fewest among all vaccination schemes that reduce the threshold parameter below 1. This is done for the situation where all model parameters are known and also for the case where parameters are estimated from an outbreak in the community prior to vaccination. It is shown that the algorithm which chooses vaccines sequentially, at each step selecting the individual which reduces the threshold parameter the most, is not in general an optimal scheme. As a consequence, explicit characterisation of the optimal scheme is only possible in certain special cases. Two different types of vaccine responses, leaky and all-or-nothing, are considered and compared for the problems mentioned above. The methods are illustrated with some numerical examples. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码:19 / 40
页数:22
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