A generic model for pandemics in networks of communities and the role of vaccination

TL;DR

This study models virus spread in interconnected communities with varying vaccination levels, revealing how unvaccinated communities can drive infections in vaccinated ones, influenced by network structure and coupling strength.

Contribution

It introduces a multi-community susceptible-vaccinated-infected-recovered model considering waning vaccine efficacy and network interactions, highlighting the unidirectional impact of unvaccinated communities.

Findings

Unvaccinated communities increase infections in vaccinated ones.

Network density affects the ability to reach disease-free states.

Gold communities maintain lower infection levels than Silver and Bronze.

Abstract

The slogan "nobody is safe until everybody is safe" is a dictum to raise awareness that in an interconnected world, pandemics such as COVID-19, require a global approach. Motivated by the ongoing COVID-19 pandemic, we model here the spread of a virus in interconnected communities and explore different vaccination scenarios, assuming that the efficacy of the vaccination wanes over time. We start with susceptible populations and consider a susceptible-vaccinated-infected-recovered model with unvaccinated ("Bronze"), moderately vaccinated ("Silver") and very well vaccinated ("Gold") communities, connected through different types of networks via a diffusive linear coupling for local spreading. We show that when considering interactions in "Bronze"-"Gold" and "Bronze"-"Silver" communities, the "Bronze" community is driving an increase in infections in the "Silver" and "Gold" communities. This shows a detrimental, unidirectional effect of non-vaccinated to vaccinated communities. Regarding the interactions between "Gold", "Silver" and "Bronze" communities in a network, we find that two factors play central role: the coupling strength in the dynamics and network density. When considering the spread of a virus in Barab\'asi-Albert networks, infections in "Silver" and "Gold" communities are lower than in "Bronze" communities. We find that the "Gold" communities are the best in keeping their infection levels low. However, a small number of "Bronze" communities are enough to give rise to an increase in infections in moderately and well-vaccinated communities. When studying the spread of a virus in a dense Erd\H{o}s-R\'enyi, and sparse Watts-Strogatz and Barab\'asi-Albert networks, the communities reach the disease-free state in the dense Erd\H{o}s-R\'enyi networks, but not in the sparse Watts-Strogatz and Barab\'asi-Albert networks. However, we also find that if all these networks...