### A Model of Social Distancing for Interacting Age-Distributed Multi-Populations: An Analysis of Students’ In-Person Return to Schools

#### Abstract

Because of the current scenario of the SARS-CoV-2 (COVID-19) pandemic in Brazil, whose vaccination campaign is in the initial stage, government authorities have pointed out towards the complete reopening of the economy. And recently for the in-personal return of classroom teaching in schools. Given the family relationship, one of the questions that remained without an answer is: What are the consequences of the schools reopening on the dissemination of COVID-19? The purpose of this work is to analyze a variant of the compartmental SIRD (Susceptible, Infected, Recovered, social distancing) model within a structured interacting age population representing six age groups from the basic education age to the elders. We present a complete analysis of the well-posedness of the proposed mathematical model. Moreover, we discuss distinct disease spreading scenarios based on observations of the mathematical behavior of the proposed dynamics. We also present a result of existence for the stationary points in terms of the parameters of the model and the number of infected age groups. Finally, we present different numerical simulations of predicted scenarios by the model. Those numerical realizations collaborate with the conclusion that an early school reopening - that implies the departure of the youngster from social isolation - causes the infection curve to grow considerably, even for other age groups.

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DOI: https://doi.org/10.5540/tcam.2022.023.04.00655

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