• Optimal treatment strategies for epidemics under explicit and endogenous budgets. • Health authority minimizes infection and costs via dynamic treatment allocation. • Quadratic and blow-up cost structures yield different epidemic and spending paths. • Extension: drug pricing modeled as a Stackelberg game with strategic responses. • Policy insights stress coordinated budget design and outcome-based pricing. Effective epidemic control policies must balance public health objectives with economic constraints, especially when deploying high-cost curative treatments for infectious diseases. This study develops an optimal control framework for a Health Authority (HA), embedded in a controlled SIR epidemic model, to minimize the societal and economic burden of infection under budget constraints. We analyze two institutional cost specifications: a quadratic cost with an explicit budget constraint and a blow-up cost with endogenous constraint enforcement. Numerical simulations calibrated to the case of hepatitis C in France illustrate how cost structures, budget design, and the health authority’s preference over the final state of the epidemic jointly influence treatment intensity, infection dynamics, and long-term health outcomes. As an extension, we incorporate a Stackelberg differential game in which a Pharmaceutical Company (PC) strategically sets the drug price, anticipating the HA’s optimal treatment response. We show that the PC’s valuation of residual infection decisively shapes price trajectories and public health outcomes. The analysis suggests that effective policies should integrate coherent budget planning, outcome-sensitive pricing schemes, and regulatory incentives to align private behavior with long-term public health objectives.
Caravaggio et al. (Tue,) studied this question.