Dynamic Systems with Fractional Derivatives Applied to Interagent Populations Problems

Abstract

The present work has as main objective to investigate the use of fractional calculus in the modeling of epidemic outbreaks of interacting populations. In particular, we propose a generalization of the SIR model with fractional derivatives to describe the dynamics of the COVID-19 epidemic outbreak in two cities with interacting populations. In special, we consider the dynamics of COVID-19 in the municipalities of Pelotas and Rio Grande, which are neighboring cities and are relatively geographically isolated from the  rest of the state of Rio Grande do Sul.