Processos estocàstics aplicats a l’epidemiologia

Abstract

The interest in human health has always been a priority for humans. Infectious diseases can produce epidemics wich are a very important cause of death in the world. The science that studies the evolution of an epidemic that affects a specific part of the population is called epidemiology. In this work, a stochastic epidemiological model SIR proposed by Henry C. Tuckwell and Ruth J. Williams in 2006 is exposed. This model uses Markov chains and a diffusion process. To be able to understand it properly, concepts of stochastic processes will be introduced and, especially, it will be explained what the stochastic integrals and stochastic differential equations are. This will be necessary to make simulations of the epidemiological model.