Analytic solutions to compartmental models of the HIV/AIDS epidemic

For many years compartmental models have provided useful insights into the spread of epidemics. Such models are usually fairly easy to set up, but eve n the simpler models have the disadvantage that they are intractable to ana lytic solution. In this paper we examine models of the HIV/AIDS epidemic, a nd show that the equations may be linearized in a piecewise manner over tim e, thus allowing analytic solutions to be obtained. Indications of the usef ulness of this approach are provided. In particular, an analytic solution g ives insight into the mechanism of the epidemic, together with a clearer pi cture of the sensitivity of results to changes in parameter values. Further , the processes of parameter estimation and the methodology of back-calcula tion also benefit from the provision of functional forms for the state vari ables.