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 Barabasi-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 Erdos-Renyi and sparse Watts-Strogatz and Barabasi-Albert networks, the communities reach the disease-free state in the dense Erdos-Renyi networks, but not in the sparse Watts-Strogatz and Barabasi-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.