On Epidemiological and Actuarial Analyses of Health Insurance Models for Communicable Diseases

Abstract

This article examines an SIDRS disease model design for insurance contracts, in which the insured population is exposed to the risks of communicable diseases. For the epidemiological models, the population is structured into four demographic groups, namely: susceptibles (S), infected PHs undergoing treatment (I), infected PHs who are diseased (D), and infected PHs who recovered (R) from the disease, with part of the latter thereafter re-entering the group of susceptibles (S) and continuing with the insurer by paying premiums until he or she is infected again. The infective class is a union of the class of those undergoing treatment, deceased policy holders (PHs), and those who have recovered. The number of deceased PHs is counted as part of the insured population because the number PHs who die of the disease must be accounted for and are entitled to claims. The insurance policies are designed for the members of the susceptible group: the latter constantly face the risk of infection and death due to the disease. The probability of PHs remaining susceptible for the SIDRS disease model is formulated. The probability density function (PDF) and cumulative distribution function (CDFs) for the SIDRS disease model for an insurance policy are obtained. For the actuarial part, we used actuarial techniques and principles to determine the financial obligations of the parties and the insurance amounts for the insurer and PHs. The cumulative insurance reserve for an annuity and a lump sum plan are also considered. To ascertain the risk of insolvency, premium adjustment for the PHs is considered. Some numerical computations of the results arising from our model analyses are also considered in this article. This article has practical applications in health insurance schemes. It is also applicable in the determination of insurance premiums payable by PHs who did not have the disease and insurance claims receivable by those who are hospitalized or die of the disease. Our model can also be practically applicable in the determination of health insurance reserves for communicable diseases.