An epidemiological model with migration for the study of Yellow Fever

Abstract

Mathematics is present in several fields of science, among them, we can highlight epidemiology, a branch that is dedicated to the study of infectious diseases. Thus, mathematics, through modeling, becomes an ally of epidemiology, through the study of mathematical models that describe the dynamics of the spread of a disease. In this work, we delimit ourselves to study a mathematical model for Yellow Fever, an acute febrile disease, transmitted by vectors (mosquitoes). Thus, this work seeks to study a compartmental model, which describes the dynamics of this disease in its different transmission cycles: wild cycle, epidemic cycle among humans who move to the forest region and urban cycle. The model also considers the presence of two different vectors, the Aedes aegypti (urban transmitter) and the Haemagogus (main transmitter in the forest region). For the study, the free equilibrium point of the disease and the basic reproduction number for each cycle were calculated. Finally, through the implementation and resolution of the equations of the model in the software Scilab, it was possible to obtain graphs of the behavior of each of the populations, enabling a more complete analysis of how the spread of the disease occurs over time.