Optimal control of structured epidemic model with vaccination strategies

The COVID-19 pandemic has underscored the importance of vaccination strategies in mitigating disease transmission and reducing mortality. This study presents an age-structured SVIJRD model incorporating vaccination and hospitalization compartments to analyze the spread of COVID-19 across different age groups. The model considers susceptible (S), vaccinated (V), infected (I), hospitalized (J), recovered (R), and decease induced death (D) populations, with interactions governed by age-specific transmission, hospitalization, and mortality rates. The objective is to determine optimal vaccination strategies that minimize infections while considering the cost of vaccination efforts. Using Pontryagin's Maximum Principle, an optimal control problem is formulated to minimize the number of infected individuals over a finite time interval. Numerical illustrations are considered using age-specific baseline values, including hospitalization rates, mortality rates, and vaccine efficacies. The findings highlight the significance of targeted vaccination strategies for different age groups in controlling the pandemic and reducing the burden on healthcare systems.