Optimal Control of Dengue under Vaccine Heterogeneity: From Dynamical Analysis to Dynamic Strategy Optimization.

The protective efficacy of dengue vaccines differs between susceptible and recovered individuals, while antibody-dependent enhancement (ADE) from vaccination may increase severe disease risk. Most studies treat ADE and vaccine allocation separately, lacking tools for dynamic cross-strategy comparison. We develop a dengue transmission model incorporating ADE effects and time delays. Using this model, we derive the basic reproduction number and establish equilibrium stability conditions. An optimal control framework is developed that integrates vaccine heterogeneity into a composite objective functional, balancing health losses, secondary infection penalties, and intervention costs. On a baseline calibrated to R0=1.515, we identify three key findings. First, targeted vaccination yields the lowest total societal cost while achieving health outcomes close to the ideal vaccine. Second, the ideal vaccine is cost-dominant when its daily price remains below $1 per capita. Third, the risky vaccine incurs higher long-term costs due to ADE-driven late-stage health loss, despite its lower procurement price. Sensitivity analysis reveals a price crossover threshold and strategy-specific responses to cost fluctuations, providing quantitative guidance for vaccine selection under varying resource constraints.