Study of math epidemiological models in piecewise smooth systems and regularization

• Grant number: 22/03800-7
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: October 01, 2022
• End date: September 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Yagor Romano Carvalho
• Supervisor: Oleg Makarenkov
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Texas at Dallas (UT Dallas), United States
• Associated to the scholarship: 21/14695-7 - Limit cycles, regularization and period function of piecewise smooth planar systems., BP.PD

Abstract

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