Vaccination intervention on epidemic dynamics in networks

TL;DR

This paper analyzes how vaccination strategies affect epidemic spread in different network structures, revealing that network topology significantly influences vaccination effectiveness and epidemic thresholds.

Contribution

It introduces an epidemic model with vaccination on various networks and examines the impact of vaccination on thresholds and prevalence, highlighting differences between small-world and scale-free networks.

Findings

Vaccination linearly reduces prevalence in small-world networks.

Vaccination exponentially reduces prevalence in scale-free networks.

Epidemic threshold depends on network type and vaccination rate.

Abstract

Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barab\'asi-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.