Minimizing Societal Cost of Epidemics: Optimal Catastrophe Insurance Compensation Allocation

ABSTRACT

This study investigates optimal strategies for allocating catastrophe insurance compensation to contain infectious disease outbreaks. We extend a classic SIR model by allowing insurance payouts to fund quarantine of infected individuals, thereby slowing transmission dynamics. We derive the basic reproduction number and analyze the existence and stability of both disease‐free and endemic equilibria. A key innovation is the linkage of real‐time with the allocation of compensation funds. We obtain a closed‐form expression for the optimal usage strategy that minimizes the real‐time during an epidemic. Our results show that compensation should be prioritized toward subpopulations with high transmission potential or high prevalence, and toward those that can be quarantined cost‐effectively. Moreover, enhancing the quarantine efficiency of compensation significantly strengthens epidemic control. The optimal strategy reduces real‐time , which in turn limits outbreak damage, lowers insurance claims, and thereby cuts premiums, ultimately minimizing the total societal cost of epidemic mitigation. This framework offers actionable insights for policymakers and advances the literature at the intersection of epidemic management and catastrophe insurance.