Ball Frank, Sirl David
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
J Math Biol. 2018 Jan;76(1-2):483-530. doi: 10.1007/s00285-017-1139-0. Epub 2017 Jun 20.
This paper is concerned with the analysis of vaccination strategies in a stochastic susceptible [Formula: see text] infected [Formula: see text] removed model for the spread of an epidemic amongst a population of individuals with a random network of social contacts that is also partitioned into households. Under various vaccine action models, we consider both household-based vaccination schemes, in which the way in which individuals are chosen for vaccination depends on the size of the households in which they reside, and acquaintance vaccination, which targets individuals of high degree in the social network. For both types of vaccination scheme, assuming a large population with few initial infectives, we derive a threshold parameter which determines whether or not a large outbreak can occur and also the probability of a large outbreak and the fraction of the population infected by a large outbreak. The performance of these schemes is studied numerically, focusing on the influence of the household size distribution and the degree distribution of the social network. We find that acquaintance vaccination can significantly outperform the best household-based scheme if the degree distribution of the social network is heavy-tailed. For household-based schemes, when the vaccine coverage is insufficient to prevent a major outbreak and the vaccine is imperfect, we find situations in which both the probability and size of a major outbreak under the scheme which minimises the threshold parameter are larger than in the scheme which maximises the threshold parameter.
本文关注的是在一个随机的易感-感染-移除模型中对疫苗接种策略的分析，该模型用于描述在一个具有随机社交联系网络且被划分为家庭的人群中流行病的传播。在各种疫苗作用模型下，我们既考虑基于家庭的疫苗接种方案，即选择个体进行疫苗接种的方式取决于他们所在家庭的规模，也考虑熟人疫苗接种，即针对社交网络中度数较高的个体。对于这两种类型的疫苗接种方案，假设人口众多且初始感染者较少，我们推导出一个阈值参数，该参数决定是否会发生大规模疫情，以及大规模疫情发生的概率和受大规模疫情感染的人口比例。对这些方案的性能进行了数值研究，重点关注家庭规模分布和社交网络度数分布的影响。我们发现，如果社交网络的度数分布是重尾的，熟人疫苗接种的表现可能会显著优于最佳的基于家庭的方案。对于基于家庭的方案，当疫苗覆盖率不足以预防大规模疫情且疫苗不完善时，我们发现，在使阈值参数最小化的方案下，大规模疫情的概率和规模都可能大于使阈值参数最大化的方案。
