A SEIRUC mathematical model for transmission dynamics of COVID-19

TL;DR

This paper introduces a new SEIRUC mathematical model for COVID-19 transmission, incorporating a convalescent state, and analyzes its stability and basic reproduction number to better understand disease dynamics.

Contribution

It proposes a novel SEIRUC model with a convalescent compartment and performs stability analysis to enhance understanding of COVID-19 transmission.

Findings

The basic reproduction number $\\mathcal{R}_0$ is derived for the model.

Stability conditions for disease-free and endemic states are established.

Graphical results validate the theoretical stability analysis.

Abstract

The world is still fighting against COVID-19, which has been lasting for more than a year. Till date, it has been a greatest challenge to human beings in fighting against COVID-19 since, the pathogen SARS-COV-2 that causes COVID-19 has significant biological and transmission characteristics when compared to SARS-COV and MERS-COV pathogens. In spite of many control strategies that are implemented to reduce the disease spread, there is a rise in the number of infected cases around the world. Hence, a mathematical model which can describe the real nature and impact of COVID-19 is necessary for the better understanding of disease transmission dynamics of COVID-19. This article proposes a new compartmental SEIRUC mathematical model, which includes the new state called convalesce (C). The basic reproduction number $\mathcal{R}_0$ is identified for the proposed model. The stability analysis are performed for the disease free equilibrium ($\mathcal{E}_0$) as well for the endemic equilibrium ($\mathcal{E}_*$) by using the Routh-Hurwitz criterion. The graphical illustrations of the proposed mathematical results are provided to validate the theoretical results.