A Modified SIS Epidemic Model with Application to Health Insurance Pricing

In this work, we investigate a modified version of the classical SIS model that incorporates hospitalization for treatment and disease-induced mortality, aiming to more accurately capture the dynamics relevant to health insurance pricing models. More precisely, we introduce a new framework, referred to as the SISHD model, which considers both hospitalized individuals and disease-induced mortality. Dynamical properties of the proposed model are thoroughly analyzed, including positivity and boundedness of the solutions, the basic reproduction number, the existence and asymptotic stability of equilibrium points. Furthermore, we utilize the proposed model in the context of health insurance pricing, where the population sizes estimated from the SISHD model are used to determine appropriate insurance costs. Finally, numerical simulations are conducted to illustrate and validate the theoretical results.