On an a priori upper bound for the time-step size for the numerical solution of epidemiological SIR-type models

da Silva M.I.; Marques J.C.; Cezaro A.D.; Conza A.O. · Computational and Applied Mathematics (2025) · DOI: 10.1007/s40314-025-03316-6

Resumen

In this work, we analyze the stiffness properties of systems of ordinary differential equations originating from the SIR-type epidemiological model. We illustrate that the stiffness effect influences the numerical approximation of the SIR-type model solution via the Euler method, contingent on the contagion rates in the classical SIR model or the presence of numerous distinct neighboring populations interacting within the SIR-type model. This highlights the necessity for an appropriate selection of time-step size in numerical approximations. We present a theoretical a priori upper bound for the Euler method’s time-step size, formulated in terms of the model parameters and the number of interacting neighboring populations, to avoid negative values in the numerical solution for the SIR-type models. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2025.

Instituciones: Universidad Nacional del Altiplano