# Vaccination dilemma on an evolving social network

## TL;DR

This paper studies how the evolving structure of social networks influences vaccination behavior and epidemic control, revealing that network dynamics can significantly affect vaccination levels and herd immunity.

## Contribution

It introduces a model of vaccination behavior on dynamic social networks, showing how network evolution impacts vaccination levels and epidemic outcomes.

## Key findings

- Higher vaccinator-infected-non-vaccinator links increase vaccination levels.
- Stronger vaccinator-healthy-non-vaccinator links also promote vaccination.
- Evolving networks can lead to higher vaccination levels than in well-mixed populations.

## Abstract

Vaccination is crucial for the control of epidemics. Yet it is a social dilemma since non-vaccinators can benefit from the herd immunity created by the vaccinators. Thus the optimum vaccination level is not reached via voluntary vaccination at times. Intensive studies incorporate social networks to study vaccination behavior, and it is shown that vaccination can be promoted on some networks. The underlying network, however, is often assumed to be static, neglecting the dynamical nature of social networks. We investigate the vaccination behavior on dynamical social networks using both simulations and mean-field approximations. We find that the more robust the vaccinator-infected-non-vaccinator links are or the more fragile the vaccinator-healthy-non-vaccinator links are, the higher the final vaccination level is. This result is true for arbitrary rationality. Furthermore, we show that, under strong selection, the vaccination level can be higher than that in the well-mixed population. In addition, we show that vaccination on evolving social network is equivalent to the vaccination in well mixed population with a rescaled basic reproductive ratio. Our results highlight the dynamical nature of social network on the vaccination behavior, and can be insightful for the epidemic control.