Qualitative and numerical analysis of epidemiological models of COVID-19 via differential equations with delay

Abstract

This research project in Mathematics uses delayed functional differential equations for the study of epidemiological models, with an emphasis on recent work on modeling the COVID-19 pandemic. It is intended to investigate such models, in their original formulations and propose modifications throughout the research, in a mathematical perspective, when considering classical issues such as existence and uniqueness of solution, stability study, existence of periodic solution and asymptotic behavior, still little addressed in the published works. Additionally, through numerical-computational simulations of epidemiological dynamics considering populations and scenarios different from those already studied, it is expected to expand the knowledge of these dynamics, especially considering the Brazilian population. (AU)