Vaccination with partial transmission and social distancing on contact networks

TL;DR

This study analyzes how partial vaccination and targeted social distancing affect epidemic spread on contact networks, revealing strategies to optimize herd immunity and reduce risk.

Contribution

It extends the cavity method to heterogeneous transmissibility, demonstrating the effectiveness of targeted social distancing over untargeted vaccination.

Findings

Partial vaccination still achieves herd immunity.

Targeted social distancing reduces epidemic risk more effectively.

Heterogeneous transmissibility influences herd immunity thresholds.

Abstract

We study the impact of vaccination on the risk of epidemics spreading through structured networks using the cavity method of statistical physics. We relax the assumption that vaccination prevents all transmission of a disease used in previous studies, such that vaccinated nodes have a small probability of transmission. To do so we extend the cavity method to study networks where nodes have heterogeneous transmissibility. We find that vaccination with partial transmission still provides herd immunity and show how the herd immunity threshold depends upon the assortativity between nodes of different transmissibility. In addition, we study the impact of social distancing via bond percolation and show that percolation targeting links between nodes of high transmissibility can reduce the risk of an epidemic greater than targeting links between nodes of high degree. Finally, we extend recent methods to compute the distributional equations of risk in populations with heterogeneous transmissibility and show how targeted social distancing measures may reduce overall risk greater than untargeted vaccination campaigns, by comparing the effect of random and targeted strategies of node and link deletion on the risk distribution.