Session S20 - Applied Math and Computational Methods and Analysis across the Americas

Monday, July 19, 19:30 ~ 20:00 UTC-3

A SIR epidemic model accounting for population mobility

Daniel Gregorio Alfaro Vigo

Universidade Federal do Rio de Janeiro, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this work, we propose a susceptible-infectious-recovered (SIR) model for the spreading of an infectious disease in a population. Our modeling uses a novel approach in order to take into account the influence of spatial heterogeneity and population mobility on disease transmission. The proposed model consist of a coupled system of three parabolic and one elliptic equations. We prove the existence and uniqueness of weak solutions of the proposed model. We also give a complete characterization of the (disease free) steady state solutions and introduce the corresponding basic reproduction number. We present several numerical examples to illustrate our theoretical results, using Galerkin/Finite Element Method for spatial discretization and finite difference time-integration schemes such as Backward-Euler and Crank-Nicolson.

Joint work with Amaury Alvarez Cruz (Universidade Federal do Rio de Janeiro).

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