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A new dynamical modeling SEIR with global analysis applied to the real data of spreading COVID-19 in Saudi Arabia

1 Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, Saudi Arabia
2 Department of Mathematics, Faculty of Applied Science, Umm Al-Qura University, Makkah, Saudi Arabia
3 College of Science and Arts, Al-Qassim University, Al Bukairiyah, Al Qassim, Saudi Arabia
4 Basic and Applied Science Institute, Arab Academy for Science, Technology, and Maritime Transport, Alexandria, Egypt
5 Science and Technology Unit (STU), Umm Al-Qura University, Makkah, Saudi Arabia

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SEIR model is a widely used and acceptable model to distinguish the outbreak of the COVID-19 epidemic in many countries. In the current work, a new proposed SEIR model as a mathematical model for the outbreak of novel coronaviruses COVID-19 will be constructed. The new proposed SEIR pandemic model provides a new vision for evaluations and management of the epidemic of COVID-19 infection. For mathematical modeling and dynamic analyses, this paper uses the real data of spreading COVID-19 in Saudi Arabia. The dynamics of the proposed SEIR model are presented with the reproduction number and the extensive stability analysis. We discussed the domain of the solution and equilibrium situation based on the proposed SEIR model by using Jacobian's method of linearization. The condition of equilibrium and its uniqueness has been proved, and the stability analysis of disease-free equilibrium has been introduced. A sensitivity analysis of the reproduction number against its internal parameters has been done. The global stability of the equilibrium of this model has been proved by using Lyapunov's Stability theorem. A numerical verification and predictions of the proposed SEIR model have been made with comparing the results based on the SEIR model and the real data due to the spreading of the COVID-19 in Saudi Arabia. The proposed SEIR model is a successful model to analyze the spreading of epidemics like COVID-19. This work introduces the ideal protocol, which can help the Saudi population to breakdown spreading COVID-19 in a fast way.
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