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The slogan "nobody is safe until everybody is safe" is a dictum to raiseawareness that in an interconnected world, pandemics such as COVID-19, requirea global approach. Motivated by the ongoing COVID-19 pandemic, we model herethe spread of a virus in interconnected communities and explore differentvaccination scenarios, assuming that the efficacy of the vaccination wanes overtime. We start with susceptible populations and consider asusceptible-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 couplingfor local spreading. We show that when considering interactions in"Bronze"-"Gold" and "Bronze"-"Silver" communities, the "Bronze" community isdriving an increase in infections in the "Silver" and "Gold" communities. Thisshows a detrimental, unidirectional effect of non-vaccinated to vaccinatedcommunities. Regarding the interactions between "Gold", "Silver" and "Bronze"communities in a network, we find that two factors play central role: thecoupling strength in the dynamics and network density. When considering thespread 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 increasein infections in moderately and well-vaccinated communities. When studying thespread of a virus in a dense Erd\H{o}s-R\'enyi, and sparse Watts-Strogatz andBarab\'asi-Albert networks, the communities reach the disease-free state in thedense Erd\H{o}s-R\'enyi networks, but not in the sparse Watts-Strogatz andBarab\'asi-Albert networks. However, we also find that if all these networks...

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