Generalization of the SIRM Epidemiological Model with Numerical Solution via Runge-Kutta for Multiple Infectious Diseases in an Interactive Environment

Abstract

This work proposes an extension and generalization of the SIRM epidemiological model, previously applied to COVID-19, to simulate the evolution of various infectious diseases. The system of ordinary differential equations is solved using the fourth-order Runge-Kutta method, known for its accuracy and stability. The developed system is implemented in the Python programming language with an interactive interface, allowing the selection of different diseases, automatic parameterization, and export of results. The goal is to provide an educational and decision-support tool for researchers and public health managers.