Mathematical Modeling of COVID-19: An Optimal Control Approach
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https://orcid.org/0000-0001-5161-7287
Abstract
A non-linear mathematical model is developed to describe the transmission dynamics of COVID-19. The model’s well-posedness is verified by analyzing the positivity and boundedness of its solutions. Analytical expressions for the disease-free equilibrium points are derived and the stability analyses of the disease-free and endemic equilibrium points are conducted. A sensitivity analysis of the model parameters with respect to the basic reproduction number (R0) is carried out to identify the key factors influencing COVID-19 transmission. Consequently, the model is extended into an optimal control problem by incorporating three time-dependent interventions: preventive measures (such as travel restrictions and personal protection), continuous vaccination of susceptible individuals, and testing, isolation, and treatment of infected cases. Four control strategies, each combining at least two interventions, are explored. The autonomous and non-autonomous systems are analyzed. Numerical simulations indicate that implementing the three control measures concurrently provides the most effective strategy to mitigating the spread of COVID-19.
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