Classic Kermack-McCendrick Model

We model the system dynamics of the HIV/AIDS epidemic by logically extending existing compartmental models [10][13]. The classical compartmental model for representing disease dynamics is the Kermack-McKendrick model, which divides a population into mutually exclusive groups that relate to specific disease states. The population is broken up into three main groups: Susceptible (S), Infected (I), and Recovered (R) to form the SIR model. Central to the concept of compartmental disease modeling methods is the idea of the transfer of individuals between states. An individual can either be removed from a state or they can join a state, and it is the interaction of these two processes that determine the system dynamics.

Our Modifications

For HIV there is no recovered state. Therefore, the recovered state is replaced by two distinct treatment states: an Antiretroviral Therapy state and a Pre-Exposure Prophylaxis state.