In December 2019, the SARS-CoV-2 (COVID-19) virus was identified and quickly spread worldwide, causing a major global health crisis. To investigate its transmission dynamics, we developed a ten-compartment mathematical model, named CoVCom10, which includes key stages such as asymptomatic (F), pre-symptomatic (E), and vaccinated (V ) individuals. The basic reproduction number (R0) has been calculated to evaluate how easily the virus can spread. We analyzed the local and global stability of the disease-free equilibrium and prove that the disease under control after vaccination when R0 < 1. A sensitivity analysis was conducted to assess the impact of key parameters, including the vaccination rate from susceptible individuals (β), trans-mission from susceptible to pre-symptomatic individuals (φ), and the rate of vaccination from pre-symptomatic individuals (γ). To evaluate intervention strategies, we extended the model by incorporating time-dependent control variables representing vaccination (a1), hospitalization (a2), and isolation of asymptomatic individuals (a3). The Pontryagin Maximum Principle was applied to identify optimal control strategies. Numerical simulations reveal that these interventions significantly reduce virus transmission, particularly as the fractional-order parameter (ς) approaches 1, which aligns with observed real-world disease dynamics. The study emphasizes the effectiveness of integrated vaccination and treatment strategies in controlling the spread of COVID-19.
Abbas et al. (2025) studied this question.