Um modelo epidemiológico para o estudo da febre amarela com interação entre ciclos urbano-silvestre

Abstract

Mathematics is present in many areas of knowledge, among them we can mention epidemiology, which is related to the study of infectious diseases. In this work, we limit ourselves to studying the mathematical modeling of Yellow Fever, an acute febrile disease, transmitted by vectors, in this case mosquitoes, the main ones being Aedes aegypti, Haemagogus and Sabethes. Generally, the disease develops in its mild form, but about 15% of cases evolve into the severe form of the disease. In Brazil, only cases of Wild Yellow Fever are recorded, since there has been no occurrence of urban transmission of the disease since 1942. Thus, this work seeks to study a compartmental mathematical model that describes the dynamics of yellow fever transmission in its different cycles: wild cycle, epidemic cycle among humans moving to the forest region and urban cycle. The model also considers the presence of two different vectors, Aedes aegypti (transmitter in the urban area) and Haemagogus (main transmitter in the forest region). For the model study, the disease-free equilibrium point was calculated, in addition to the basic reproduction number (R0) for each of the transmission cycles. Also, equilibrium points were calculated for three different cases, considering different means of virus circulation. Finally, through the computational simulation, it was possible to obtain a graph for each studied compartment, allowing a more complete analysis of how the disease spreads over time. Also, to validate the model, a real case of an outbreak of Yellow Fever occurred in Luanda, Angola, in early 2016 was implemented. In this case, the number of infected people and the impact of vaccination in mitigating the outbreak were simulated.