Guillaume Batallie (University of Luxembourg): «The pandemic game : Vaccination, Treatment, and Eradication Incentives.»

Abstract: Epidemic management typically combines public prevention policies with privately supplied treatments. While most existing studies analyze disease control from the perspective of a social planner, actual health-care systems often separate these responsibilities between governments and pharmaceutical firms. This paper develops acontinuous-time SIS epidemic model with vaccination and treatment to examine how such institutional separation affects epidemic dynamics

and disease eradication.

We first characterize the socially efficient benchmark, which may exhibit endemic steady states, path dependence, and Sethi–Skiba thresholds. We then study a differential game in which a government chooses vaccination while a pharmaceutical firm determines treatment intensity. We identify a robust incentive threshold that governs treatment behavior near the disease-free state. This threshold generates a last-mile eradication problem: for a range of values of the transmission rate, disease eradication remains technologically feasible and socially desirable, but it is not selected in equilibrium because treatment providers value the future demand

generated by continued infections. Consequently, decentralized incentives may sustain endemic disease even when coordinated intervention would eradicate it.

Finally, we examine regulatory policies designed to correct this distortion. We show that conventional treatment subsidies fail to eliminate the underlying incentive conflict, whereas prevalence-based and treatment-compliance contracts can restore eradication incentives. The results highlight how the organization of health-care systems influences long-run epidemiological outcomes through the interaction between public-health objectives and private treatment incentives.