Model for prognostic of symptomatic, asymptomatic and hospitalized COVID-19 cases with correct demography evolution

TL;DR

This paper introduces a modified SEIR model incorporating demographic changes and distinguishes symptomatic, asymptomatic, and hospitalized COVID-19 cases, providing theoretical analysis and fitting real data from Cuba.

Contribution

It develops a novel SEIR model with population growth effects and analyzes its stability, offering a more realistic framework for COVID-19 epidemic modeling.

Findings

Model accurately fits COVID-19 data from Cuba

Reproduction number $R_0$ determines disease extinction or persistence

Population growth affects epidemic dynamics significantly

Abstract

The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the behaviour of symptomatic, asymptomatic and hospitalized patients of COVID-19 epidemic, including the effect of demographic variation of population. It is shown that considering a population growth proportional to the total population leads to solutions with a qualitative behaviour different from the behaviour obtained in many studies, where constant growth ratio is assumed. An exhaustive theoretical study is carried out and the basic reproduction number $R_0$ is computed from the model equations. It is proved that if $R_0<1$ then the disease-free manifold is globally asymptotically stable, that is, the epidemics remits. Global and local stability of the equilibrium points is also studied. Numerical simulations are used to show the agreement between numerical results and theoretical properties. The model is fitted to experimental data corresponding to the pandemic evolution in the Rep\'ublica de Cuba, showing a proper behaviour of infected cases which let us think that can provide a correct estimation of asymptomatic cases. In conclusion, the model seems to be an adequate tool for the study and control of infectious diseases in particular the COVID-19 disease transmission.