Modeling and Optimal Control of Infectious Diseases With Information's Impact on Behavioural Change and on Vaccination Under Saturated Medical Environment and Time Delays in Controls

ABSTRACT Optimal allocation of limited resources is essential for effective disease control. In this study, we develop and analyse an optimal control model to evaluate the economic and epidemiological impact of three interventions: information‐induced self‐protection (behavioural change), information‐induced vaccination, and saturated treatment when there is a short‐term immune class of individuals. Using Pontryagin's Maximum Principle and numerical simulations, we compare different control strategies and identify the most efficient policies. Our results indicate that the comprehensive approach of all control measures is the most feasible policy to balance the disease prevalence and the economic burden, while the other combinations have different impacts depending on available resources. Further, cost‐effectiveness analysis using ACER, IAR, and ICER indicates that information‐induced vaccination is the most economically efficient policy. We also examine the criticality of the basic reproduction number on disease burden and show that policy performance differs between mild and severe epidemic scenarios. The role of implementation delays is also evaluated through time‐series dynamics, the reproduction number variations, and cost‐effectiveness outcomes. Finally, sensitivity analysis highlights key parameters that significantly shape the disease dynamics and control impact.