Equações diferenciais e modelagem matemática: uma proposta de ensino da função exponencial no estudo da dengue

Abstract

This paper presents a proposal of activities for the study of dengue cases in the city of Sorocaba-SP in the years 2023 and 2024, in addition to a projection for 2025. The study was carried out through mathematical modeling, using the Malthusian model, in spreadsheet software. The functions that represent the growth of dengue cases were obtained as solutions of Ordinary Differential Equations. In view of this, a brief study was carried out on Differential Equations, with emphasis on first-order ones. The modeling used was based on the mathematical model of Thomas Robert Malthus, the Malthusian model, applied to the problem of dengue fever. In addition, a brief report on dengue fever was presented, addressing its discovery in Brazil, transmission, symptoms, diagnosis, prevention and treatment. The National Common Curricular Base (BNCC) was also explored, focusing on the five specific competencies of Mathematics and its Technologies for High School, as well as associated skills. Finally, focusing on dengue cases in the city of Sorocaba in the years 2023, 2024 and a study for 2025, a sequence of didactic activities aimed at teaching exponential functions through contextualized situations is proposed, promoting meaningful learning and the development of students’ mathematical thinking.