Application of the criterion of Li-Wang to a five dimensional epidemic model of COVID-19. Part I

TL;DR

This paper applies the Li-Wang stability criterion to analyze the stability of a five-dimensional COVID-19 epidemic model, focusing on the disease-free and endemic equilibria, and sets the stage for control strategies in Part II.

Contribution

It introduces the use of the Li-Wang criterion on second additive compound matrices to study stability of a complex COVID-19 model, extending previous methods.

Findings

Established stability conditions for disease-free equilibrium

Identified criteria for endemic equilibrium stability

Provided technical calculations and theoretical framework

Abstract

The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon. If the basic reproduction number R0 is below unity, the disease-free equilibrium P0 is globally stable in the feasible region and the disease always dies out. If R0 > 1, a unique endemic equilibrium P? is globally asymptotically stable in the interior of the feasible region and the disease will persist at the endemic equilibrium if it is initially present. In this paper (Part I), we reinvestigate the study of the stability or the non stability of a mathematical Covid-19 model constructed by Nita H. Shah, Ankush H. Suthar and Ekta N. Jayswal. We use a criterion of Li-Wang for stability of matrices [Li-Wang] on the second additive compound matrix associated to their model. In second paper (Part II), In order to control the Covid-19 system, i.e., force the trajectories to go to the equilibria we will add some control parameters with uncertain parameters to stabilize the five-dimensional Covid-19 system studied in this paper. Based on compound matrices theory, we apply in [Intissar] again the criterion of Li-Wang to study the stability of equilibrium points of Covid-19 system with uncertain parameters. In this part II, all sophisticated technical calculations including those in part I are given in appendices.