Design and Financial Analysis of a Health Insurance Based on an SIH-Type Epidemic Model

We present a design and financial analysis of a health insurance based on an SIH-type epidemic model. Specifically, we first construct the model in a continuous form, study its dynamical properties, and formulate the financial quantities involved in our insurance. Subsequently, we discretise the model using the forward Euler method, study the dynamical properties of the resulting discrete model, and formulate discrete analogues of the above financial quantities. We conduct a numerical simulation using two sets of parameter values, each representing a disease-free and an endemic scenario, which reveals that in the latter scenario, the insurance's gross premium is higher, the insurer's minimum loss-preventing start-up capital is lower, and the insurer's total profit is higher, compared to the corresponding values in the former scenario. Finally, through a sensitivity analysis, we show that in both scenarios, the disease's basic reproduction number, the gross premium, the minimum start-up capital, and the total profit depend most sensitively on the population's natural death coefficient, the disease's incidence coefficient, the hospitalisation benefit, and the premium surcharge percentage allocated to profit, respectively.