A multi-stage compartmental model for HIV-infected individuals: I--waiting time approach

Traditionally, epidemic processes have focused on establishing systems of differential-difference equations governing the number of individuals at each stage of the epidemic. Except for simple situations such as when transition rates are linear, these equations are notoriously intractable mathematically. In this work, the process is described as a compartmental model. The model also allows for individuals to go directly from any prior compartment directly to a final stage corresponding to death. This allows for the possibility that individuals can die earlier due to some non-disease related cause. Then, the model is based on waiting times in each compartment. Survival probabilities of moving from a given compartment to another compartment are established. While our approach can be used for general epidemic processes, our framework is for the HIV/AIDS process. It is then possible to establish the impact of the HIV/AIDS epidemic process on, e.g., insurance premiums and payouts and health-care costs. The effect of changing model parameter values on these entities is investigated.