Modelización y Simulación del COVID-19 con Ecuaciones Diferenciales Estocásticas

Abstract

[SPA]En este trabajo se analizará la evolución de la pandemia COVID-19 mediante un modelo SDE (en ecuaciones diferenciales estocásticas) con un sistema de tipo SIRD (Susceptibles-Infectados-ResistentesMuertos). Simularemos este modelo usando Matlab y estudiaremos los resultados obtenidos, justificándolos a partir de la teoría y analizaremos los resultados obtenidos. [ENG]Stochastic modelling has come to play a very important role in economics and virtually any other branches of science where differential equations cannot relate accurately to the reality of certain events. In this paper, we are going to study the evolution of the COVID-19 pandemic using a SDE (stochastic differential equation) model to portray a SIRD (Susceptible-Infected-Resistant-Dead) system. The aim of this work is to introduce the reader to SDE theory at an introductory level and then to carry that knowledge onto Matlab in order to correlate theory and experimental results. First, we will introduce the theory needed to understand the simulations and the models that will be used on the next chapter. Then, the results will be analyzed and discussed on the bases of the previous explained theory. This methodology will be followed throughout the whole text, excluding the last chapter, where personal opinions will be given regarding the whole paper and the most significant results. We are going to simulate a specific model using Matlab to obtain simulation results. These are analyzed on the bases of the SDE theory that was explained in the previous chapter. Finally, the conclusions will be drawn from our results to prove whether the practical use of stochastic differential equations are useful in a population system model or not.