Analytic solutions to compartmental models of the HIV/AIDS epidemic

For many years compartmental models have provided useful insightsinto the spread of epidemics. Such models are usually fairlyeasy to set up, but even the simpler models have the disadvantagethat they are intractable to analytic solution. In this paperwe examine models of the HIV/AIDS epidemic, and show that theequations may be linearized in a piecewise manner over time,thus allowing analytic solutions to be obtained. Indicationsof the usefulness of this approach are provided. In particular,an analytic solution gives insight into the mechanism of theepidemic, together with a clearer picture of the sensitivityof results to changes in parameter values. Further, the processesof parameter estimation and the methodology of back-calculationalso benefit from the provision of functional forms for thestate variables.