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

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 a central role: the coupling strength in the dynamics and network density. When considering the spread of a virus in Barabási–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 dense Erdős–Rényi and sparse Watts–Strogatz and Barabási–Albert networks, the communities reach the disease-free state in the dense Erdős–Rényi networks, but not in the sparse Watts–Strogatz and Barabási–Albert networks. However, we also find that if all these networks are dense enough, all types of communities reach the disease-free state. We conclude that the presence of a few unvaccinated or partially vaccinated communities in a network can increase significantly the rate of infected population in other communities. This reveals the necessity of a global effort to facilitate access to vaccines for all communities.