Speaker: Fernando Baltazar Larios, Universidad Nacional Autónoma de México

Date and Time: Wednesday, December 7, 2022 - 2:00pm to 3:00pm

Abstract

In this talk, I present a stochastic model for epidemiology data. The proposed model is obtained as a random perturbation of a suitable parameter in a deterministic SEIR system. This perturbation allows us to obtain a set of coupled stochastic differential equations (SDEs) that still have the conservation law. Afterward, we calculate the maximum likelihood estimation (MLE) for parameters that represent the symptomatic infection rate, asymptomatic infection rate, and the proportion of symptomatic individuals. We prove the consistency of the MLE for a fixed time observation window, in which the disease is in its growth phase.

The proposed stochastic SEIR model improves the uncertainty quantification of an overestimated MCMC scheme based on its deterministic model to count reported-confirmed COVID-19 cases of Mexico City. Using a particular mechanism to manage missing data, we developed MLE for some parameters of the stochastic model that improves the description of variance of the actual data.

Bio

Bachelor of Actuary and Ph.D. in mathematical sciences from the National Autonomous University of Mexico (UNAM) with a research stay at the University of Copenhagen, Denmark. Full-time professor-researcher of the Department of Mathematics of the Faculty of Sciences of the UNAM since 2012. I have been the coordinator of the Bachelor of Actuary of the Faculty of Sciences of the UNAM and the area of Mathematical Finance in the Graduate of Mathematical Sciences of the UNAM. My main lines of research are applied probability and statistical estimation of stochastic processes in areas such as Mathematical Finance, Risk Theory, Epidemiology, and Biology.