Working Paper Article Version 1 This version is not peer-reviewed

# A Novel Mathematical Model (SEIRQ) of the COVID-19 Epidemic: Assessing the Epidemiological Rates of Diseases Spread in Saudi Arabia

Version 1 : Received: 10 July 2020 / Approved: 12 July 2020 / Online: 12 July 2020 (12:14:17 CEST)

How to cite: Youssef, H.; Alghamdi, N.; Ezzat, M.A.; El-Bary, A.A.; Shawky, A.M. A Novel Mathematical Model (SEIRQ) of the COVID-19 Epidemic: Assessing the Epidemiological Rates of Diseases Spread in Saudi Arabia. Preprints 2020, 2020070253 Youssef, H.; Alghamdi, N.; Ezzat, M.A.; El-Bary, A.A.; Shawky, A.M. A Novel Mathematical Model (SEIRQ) of the COVID-19 Epidemic: Assessing the Epidemiological Rates of Diseases Spread in Saudi Arabia. Preprints 2020, 2020070253

## Abstract

This article aims to construct a new epidemic mathematical model for the outbreak of the novel coronavirus COVID-19. The SEIRQ pandemic model provides a new approach for evaluations and management of the COVID-19 epidemic. For mathematical modeling and dynamic analyses, this paper uses real data surrounding the spread of COVID-19 in Saudi Arabia. The dynamics of the SEIRQ model are presented with the reproduction number and with extensive stability analysis. We discuss the domain of the solution and equilibrium situation based on the SEIRQ model by using a Jacobian method of linearization. The condition of equilibrium and its uniqueness has been proven, and the stability analysis of disease-free equilibrium has been introduced. A sensitivity analysis of the reproduction number against its internal parameters has been achieved. The global stability of the equilibrium of the new model has been proven by using the Lyapunov stability theorem. A numerical verification and predictions of the SEIRQ model have been provided by comparing the results based on the SEIRQ model with real data on the spread of COVID-19 in Saudi Arabia. The outcome of this work reveals that the SEIRQ model is a successful model for analyzing the spread of epidemics, such as COVID-19. At the end of this work, we introduce an ideal protocol that can help the Saudi population quickly stop the spread of COVID-19.

## Subject Areas

COVID-19; Jacobian matrix; Lyapunov stability; Novel coronavirus; Reproduction number; SEIR model; SEIRQ model