Study of math epidemiological models in piecewise smooth systems and regularization

Abstract

Despite the huge relevance of vaccines for preventing infectious diseases, physical isolationfor susceptible individuals and quarantine of infected individuals also are key strategies tofight against a pandemic. Based on math epidemiological models are governed by piecewise smooth systems, we are interested in anintermittent non-pharmacological protocol to control the fraction of infected individuals andsusceptible individuals. Our main goal in this project is to provide a global analysis ofthe model, giving qualitative information about every initial condition, investigating theexistence of some bifurcations, and possibly predicting conditions so do not to collapse thehealth system. In the first case, we will analyze planar piecewise smooth systems definedin two zones separated by a straight line. And, in the other case, we work with a planarpiecewise smooth system with singular borders with four zones. In addition, we are intendingto approach these models or systems through a smoothing process.