Abstract

In face of the epidemic risk, the catastrophe insurance plan is an effective way to transfer risk and alleviate the shortage of resources. The payment of catastrophe insurance compensation is usually based on certain principles, and different payment and use strategies of compensation will affect the effect of epidemic mitigation measures, which in turn affects the subsequent evolution of the epidemic and compensation payment. Based on the epidemiological model, this paper studies the optimal usage strategy of catastrophe insurance compensation that minimizes the real-time reproduction number. First, we constructed an epidemic model that considers multiple types of infected populations. We give the basic reproduction number $R_0$, and analyze the existence and stability of disease-free and endemic equilibrium and the persistence of epidemics. Then, we introduce an pandemic catastrophe insurance plan whose compensation payment principle is based on the number of new infections per day. Next, we give the optimal compensation usage strategy, and then analyze the monotonic relationship between the optimal strategy and important epidemiological parameters. Finally, we show the conclusions intuitively through numerical simulations. Our results can provide suggestions for policymakers to implement real-time epidemic tracking and control.