An optimal control vaccine model of COVID-19 with cost-effective analysis

This study presents a comprehensive COVID-19 vaccination model, integrating breakthrough transmission, and evaluates its efficacy through various analytical techniques. To assess secondary infections, four effective reproduction rates are computed corresponding to different disease states. The sensitivity analysis of the reproduction rates is conducted using the PRCC to identify influential compartments and parameters. The model is extended to incorporate five time-dependent control interventions to reduce infected compartments, with optimisation performed using the Pontryagin maximum principle. A cost-effectiveness analysis of these strategies is conducted using the average cost-effectiveness ratio. Analysis shows that the model does not undergo backward bifurcation, meaning a stable disease-free equilibrium cannot coexist with a stable endemic equilibrium. The findings show that strict adherence to standard operating procedures is the most effective single intervention. In contrast, a combined approach incorporating all five control interventions is the most effective in averting infections with the lowest ACER.