Abstract
This note considers the spread of HIV in a single prison where there is a constant rate of departure and replacement of prisoners. Some of the incoming prisoners will be HIV +, and homogeneous mixing within the prison is assumed. HIV is thus spread sexually or by the sharing of intravenous drug users' needles. A deterministic continuous time prison model is examined, and the number of HIV+ infective prisoners at time t derived. A stochastic analogue of this model is constructed, in the form of a continuous Markov chain, and its embedded chain studied. Finally, a control procedure involving the screening of a proportion of the incoming prisoners, and the quarantining of the HIV+ individuals is proposed. Its consequences are derived for the deterministic model. The proportion to be screened, given a total expenditure for the screening procedure and the medical costs of quarantined and non-quarantined infectives, can be calculated.
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