Some actuarial mathematical models for insuring the susceptibles of a communicable disease
Abstract
Using epidemiological and actuarial analysis, this paper formulates some new actuarial mathematical models, called S-I-DR-S models, for insuring the susceptibles of a population exposed to a communicable disease. Epidemiologically, the population is structured into four demographic groups, namely: susceptibles (S), infectives (I), diseased (D) and recovered (R), with the latter automatically re-entering the group of susceptibles (S). The insurance policies are targeted at the members of the susceptible group who face the risk of infection and death due to the disease. Using actuarial techniques and principles, we determine some interesting features of the model, namely, (a) financial obligations of the parties, (b) present value of premiums, (c) quantum of claims by infected policy holders (PHs), (d) quantum of claims on behalf of deceased PHs, (e) cumulative insurance reserve for annuity and (f) lump sum plan. To check the risk of insolvency, premium adjustment for the PHs is also considered.
