ABSTRACT
The Susceptible-Exposed-Infectious-Recovered (SEIR) model is an established and appropriate approach in many countries to ascertain the spread of the coronavirus disease 2019 (COVID-19) epidemic. We wished to create a new COVID-19 model to be suitable for patients in any country. In this work, a modified SEIR model was constructed. We used the real data of COVID-19 spread in Saudi Arabia for statistical analyses and complex analyses. The reproduction number and detailed review of stability demonstrated the complexities of our proposed SEIR model. The solution and equilibrium condition were explored based on Jacobian's linearization approach to the proposed SEIR model. The state of equilibrium was demonstrated, and a stability study was conducted in the disease-free environment. The reproduction number was measured sensitively against its internal parameters. Using the Lyapunov principle of equilibrium, the overall consistency of balance of our model was demonstrated. Findings using the SEIR model and observed outcomes due to COVID-19 spread in Saudi Arabia were compared. The modified SEIR model could enable successful analyses of the spread of epidemics such as COVID-19. An "ideal protocol" comprised essential steps to help Saudi Arabia decelerate COVID-19 spread. The most important aspects are to stay at home as much as possible and for infected people to remain in an isolated zone or secure area.
ABSTRACT
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.