Uma Solução Semianalítica de Modelos Compartimentais Simples para transmissão de doenças infecciosas

Abstract

In this work, we propose a semi-analytical solution for Simple Compartmental Models, more specifically for the SIR Model. From the system of ordinary differential equations itself, with a change of variable through an extended domain-based mapping, we seek to build a sharing of solutions paths through a field function, generated by a partial differential equation. Using the characteristic method, we obtain the exact solution of this function in terms of an arbitrary function whose argument is in integral form. Since the resulting integral has no exact solution, a suitable Newton Cotes quadrature is used and the original system variables are reconstructed by the respective variable changes. Hypothetical simulations are proposed to analyze the plausibility and satisfaction of initial, limit, and final conditions of populations