Exploring epidemic dynamics: study of a compartmental model and its applications

The present study addresses the importance of mathematical modeling in understanding and preventing pandemics, focusing on a Susceptible-Infected-SusceptibleInfected-Recovered model. This compartmental model, an extension of the classic SIR model, incorporates the possibility of reinfection and intermediate stages of susceptibility, as well as considering competition between different viral variants. The study proposes and analyzes the model, investigating its intrinsic properties such as equilibrium around a critical point and calculation of the basic reproduction number. Additionally, the model is applied in the city of Manaus during a critical period of the COVID-19 pandemic, allowing for a practical evaluation of its effectiveness in understanding disease dynamics and developing control strategies. The results obtained demonstrate that the model enriches the understanding of COVID-19 epidemiology, providing crucial insights for planning targeted interventions adapted to the specific characteristics of circulating variants. Furthermore, the model contributes to didactic debates on dynamic systems, expanding knowledge on the spread of infectious diseases and the importance of mathematical modeling in public health.

Keywords:
COVID-19; pandemic; dynamic systems; variants; compartmental models