A Discrete-Time Compartmental Epidemiological Model for COVID-19 with a Case Study for Portugal

TL;DR

This paper introduces a discrete-time epidemiological model for COVID-19, demonstrating its global stability and validating it with real data from Portugal, providing a useful tool for understanding disease dynamics.

Contribution

It develops a discrete-time version of a COVID-19 model and proves its global stability, extending previous continuous-time analyses with numerical validation.

Findings

The discrete model's DFE is globally stable.

Numerical simulations align with theoretical predictions.

Model accurately reflects COVID-19 spread in Portugal.

Abstract

In [Ecological Complexity 44 (2020) Art. 100885, DOI: 10.1016/j.ecocom.2020.100885] a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) is presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) is analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COVID-19 real data, we show, through numerical simulations, the consistence of the obtained theoretical results.