Approximate Analytical Solution of an Extended COVID-19 Model Incorporating Two-Dose Vaccination and Physical Control Measures

The COVID-19 pandemic, which severely disrupted the global economy, remains a vital area of study for effective preparedness against future epidemics. The emergence of different variants has led to successive waves of the disease, prompting the development of numerous mathematical models. This study investigates an extended COVID-19 model that incorporates both first and second doses of vaccination as control strategies, alongside previously established physical preventive measures. The model is demonstrated to be mathematically and epidemiologically well-posed, with the existence and uniqueness of solutions to the state system established prior to analysis. Using the Next-Generation Matrix method, the control reproduction number was derived. Analytical results indicate that the disease-free equilibrium is locally and globally asymptotically stable when the control reproduction number, RcR_cRc, is less than one, and unstable when it exceeds one. Sensitivity analysis was conducted to determine the influence of key parameters on Rc. Findings highlight that improving compliance with hand sanitizing, social distancing, mask usage, testing, isolation, and vaccination significantly aids disease control. Conversely, reducing the rate of contact with exposed individuals, infectiousness development, and transmission probabilities also contributes to containment. Numerical simulations further illustrate the impact of these control measures, emphasizing the effectiveness of vaccination and adherence to physical protocols. The study recommends promoting vaccination and reinforcing compliance with physical preventive measures to mitigate the spread of COVID-19.