Assessing the Impact of Time-Varying Optimal Vaccination and Non-Pharmaceutical Interventions on the Dynamics and Control of COVID-19: A Computational Epidemic Modeling Approach

Yan Li, Samreen, Laique Zada (), Emad A. A. Ismail, Fuad A. Awwad and Ahmed M. Hassan
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Yan Li: School of Mathematics and Data Sciences, Changji University, Changji 831100, China
Samreen: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Laique Zada: Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan
Emad A. A. Ismail: Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
Fuad A. Awwad: Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
Ahmed M. Hassan: Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt

Mathematics, 2023, vol. 11, issue 20, 1-25

Abstract: Vaccination strategies remain one of the most effective and feasible preventive measures in combating infectious diseases, particularly during the COVID-19 pandemic. With the passage of time, continuous long-term lockdowns became impractical, and the effectiveness of contact-tracing procedures significantly declined as the number of cases increased. This paper presents a mathematical assessment of the dynamics and prevention of COVID-19, taking into account the constant and time-varying optimal COVID-19 vaccine with multiple doses. We attempt to develop a mathematical model by incorporating compartments with individuals receiving primary, secondary, and booster shots of the COVID-19 vaccine in a basic epidemic model. Initially, the model is rigorously studied in terms of qualitative analysis. The stability analysis and mathematical results are presented to demonstrate that the model is asymptotically stable both locally and globally at the COVID-19-free equilibrium state. We also investigate the impact of multiple vaccinations on the COVID-19 model’s results, revealing that the infection risk can be reduced by administrating the booster vaccine dose to those individuals who already received their first vaccine doses. The existence of backward bifurcation phenomena is studied. A sensitivity analysis is carried out to determine the most sensitive parameter on the disease incidence. Furthermore, we developed a control model by introducing time-varying controls to suggest the optimal strategy for disease minimization. These controls are isolation, multiple vaccine efficacy, and reduction in the probability that different vaccine doses do not develop antibodies against the original virus. The existence and numerical solution to the COVID-19 control problem are presented. A detailed simulation is illustrated demonstrating the population-level impact of the constant and time-varying optimal controls on disease eradication. Using the novel concept of human awareness and several vaccination doses, the elimination of COVID-19 infections could be significantly enhanced.

Keywords: COVID-19 pandemic; multiple vaccine doses; sensitivity analysis; time-varying optimal controls; Pontryagin maximum principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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