Abstract
This paper is concerned with the analysis of vaccination strategies in a stochastic susceptible rightarrow infected rightarrow 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.
Highlights
Introduction and description of resultsMathematical models for the spread of infectious disease have much to offer in terms of understanding past outbreaks, predicting likely behaviours of future outbreaks and predicting the effect of interventions or mitigating strategies
Particular attention has been paid to the analysis of acquaintance vaccination, which aims to target vaccination at individuals who are highly connected in the network
We find that acquaintance vaccination potentially offers substantial benefits over other vaccine allocation regimes
Summary
Introduction and description of resultsMathematical models for the spread of infectious disease have much to offer in terms of understanding past outbreaks, predicting likely behaviours of future outbreaks and predicting the effect of interventions or mitigating strategies. If the vaccine is perfect the early stages and final outcome of an epidemic with this acquaintance vaccination model can be analysed relatively using branching process approximations This is because the epidemic involves only unvaccinated individuals, and the degrees of the neighbours of an unvaccinated individual are mutually independent. Infinite-type branching processes are required if the support of D is countably infinite For these reasons, Ball and Sirl (2013) introduced an alternative acquaintance vaccine allocation model and analysed it, in the setting of a standard network model (without households). We extend this analysis to the present network and households model
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