Assessing the spatio-temporal spread of COVID-19 via compartmental models with diffusion in Italy, USA, and Brazil

TL;DR

This paper evaluates a PDE-based compartmental model for COVID-19 spread across Italy, USA, and Brazil, demonstrating its robustness and accuracy in reproducing real-world spatial-temporal epidemic data.

Contribution

It extends previous PDE SEIRD models by validating their robustness across diverse geographical regions and longer periods, confirming their effectiveness in modeling COVID-19 dynamics.

Findings

Model accurately reproduces COVID-19 spread in Italy, USA, and Brazil

PDE SEIRD models show robustness over extended periods and different geometries

Results align well with real epidemiological data across regions

Abstract

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation (ODE) models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased (SEIRD) framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.