Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure

TL;DR

This paper analyzes vaccination strategies in a stochastic SIR epidemic model on random networks with household structure, deriving thresholds for outbreaks and comparing the effectiveness of household-based and acquaintance vaccination schemes.

Contribution

It introduces a comprehensive analysis of vaccination strategies considering household and social network structures, deriving outbreak thresholds and comparing their effectiveness.

Findings

Acquaintance vaccination outperforms household-based schemes on heavy-tailed networks.

Threshold parameters determine outbreak potential and are derived for different vaccination schemes.

In some cases, less optimal schemes can lead to larger outbreaks when vaccine coverage is insufficient.

Abstract

This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible $\to$ infected $\to$ 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 and fraction of the population infected by such an 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 \emph{larger} than in the scheme which maximises the threshold parameter.