Modelling the spread of HIV in prisons

This paper is concerned with models for the spread of HIV in prisons. We first consider a single prison of size N in which there is homogeneous mixing, and where there is an inflow and outflow of n< N prisoners at times t= 0, 1, 2,... Conditions are derived for the stability of the system. The interaction of such a prison with the outside world is then studied, and stability conditions obtained for this case. Finally, a quarantine policy is examined and its cost analyzed, both in the non-stable and stable cases.