Simulación numérica para dos modelos tipo sir y seir que describen al covid-19 a través de los métodos multipasos

Abstract

Multi-step methods constitute crucial tools in the analysis and resolution of systems of differential equations. However, often they are overlooked in favor of classical methods to solve these systems. To describe and analyze the spread of the COVID-19 virus, multi-step methods are used to improve the accuracy and computational efficiency of the simulations. The methodology employed was of a mixed approach, incorporating both qualitative and quantitative elements. Qualitatively, the study engages with the theoretical framework concerning the existence and uniqueness of solutions for Ordinary Differential Equation. Quantitatively, the investigation uses algorithms and numerical analysis of the models to observe the behavior of the disease. The practical implementation is carried out by simulating specific scenarios of virus spread, considering several variables such as infection rates, incubation, and recovery periods. Detailed comparisons are made between the SIR and SEIR models, assessing their capacity to predict the evolution of the disease. The results obtained demonstrate the effectiveness of multi-step methods in the numerical simulation of these epidemiological models. Furthermore, some valuable demonstrations are presented for understanding applied mathematics