A New Compartmental Epidemiological Model for COVID-19 with a Case Study of Portugal

TL;DR

This paper introduces a new seven-equation compartmental model for COVID-19 in Portugal, validated with real data, providing insights into disease spread and the basic reproduction number during the pandemic.

Contribution

The paper presents a novel compartmental model with stability analysis and real data fitting, enhancing understanding of COVID-19 dynamics in Portugal.

Findings

Model accurately fits active and hospitalized cases with low error

Basic reproduction number aligns with official estimates

Mathematical analysis confirms model positivity and boundedness

Abstract

We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of emergency. New results include the compartmental model, described by a system of seven ordinary differential equations; proof of positivity and boundedness of solutions; investigation of equilibrium points and their stability analysis; computation of the basic reproduction number; and numerical simulations with official real data from the Portuguese health authorities. Besides completely new, the proposed model allows to describe quite well the spread of COVID-19 in Portugal, fitting simultaneously not only the number of active infected individuals but also the number of hospitalized individuals, respectively with a $L^2$ error of $9.2152e-04$ and $1.6136e-04$ with respect to the initial population. Such results are very important, from a practical point of view, and far from trivial from a mathematical perspective. Moreover, the obtained value for the basic reproduction number is in agreement with the one given by the Portuguese authorities at the end of the emergency states.