The critical vaccination fraction for heterogeneous epidemic models
The critical vaccination fraction for heterogeneous epidemic models
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DOI：
10.1016/s0025-5564(02)00129-3
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发表时间：
2003-01-01
影响因子：
4.3
通讯作者：
Longini, IM
中科院分区：
文献类型：
--
作者：
Hill, AN;Longini, IM
给定具有m个异质亚群的种群，开发了一种方法，通过将繁殖数设置为1来确定预防流行病的最小疫苗分配。该框架具有足够的普遍性，可适用于若干流行病情况，例如具有重要动态的SIR、SEIR和SIS模型。再现数是线性化系统在模型局部平衡点附近的最大特征值。利用Perron-Frobenius定理，给出了一种生成解的精确方法，并证明了临界疫苗分配的阈值曲面是正则（m - 1）维流形的紧连子集。对具有两个亚群的人口进行全面检查。阈值曲线要么是双曲线，要么是直线。给出了当在多群体人群中仅接种一个或两个群体就可实现阈值消除的明确条件，并推导出临界覆盖率的表达式。特别提到了A型流感模型。分离或比例混合也处理。对阈值曲面的凸性条件进行了推测，并讨论了在阈值曲面上保持疫苗用量最小的问题。(C) 2003爱思唯尔科学有限公司版权所有。
Given a population with m heterogeneous subgroups, a method is developed for determining minimal vaccine allocations to prevent an epidemic by setting the reproduction number to 1. The framework is sufficiently general to apply to several epidemic situations, such as SIR, SEIR and SIS models with vital dynamics. The reproduction number is the largest eigenvalue of the linearized system round the local point of equilibrium of the model. Using the Perron-Frobenius theorem, an exact method for generating solutions is given and the threshold surface of critical vaccine allocations is shown to be a compact, connected subset of a regular (m - 1)-dimensional manifold. Populations with two subgroups are examined in full. The threshold curves are either hyperbolas or straight lines. Explicit conditions are given as to when threshold elimination is achievable by vaccinating just one or two groups in a multi-group population and expressions for the critical coverage are derived. Specific reference is made to an influenza A model. Separable or proportionate mixing is also treated. Conditions are conjectured for convexity of the threshold surface and the problem of minimizing the amount of vaccine used while remaining on the threshold surface is discussed. (C) 2003 Elsevier Science Inc. All rights reserved.