A multi-stage compartmental model for HIV-infected individuals: II – Application to insurance functions and health-care costs

•Multi-stage waiting time models for HIV/AIDS individuals.•Impact on insurance premiums.•Impact on life annuity policies.•Health-care costs.

Stochastic population processes have received a lot of attention over the years. One approach focuses on compartmental modeling. Billard and Dayananda (2012) [1] developed one such multi-stage model for epidemic processes in which the possibility that individuals can die at any stage from non-disease related causes was also included. This extra feature is of particular interest to the insurance and health-care industries among others especially when the epidemic is HIV/AIDS. Rather than working with numbers of individuals in each stage, they obtained distributional results dealing with the waiting time any one individual spent in each stage given the initial stage. In this work, the impact of the HIV/AIDS epidemic on several functions relevant to these industries (such as adjustments to premiums) is investigated. Theoretical results are derived, followed by a numerical study.