How bad can it get? Bounding worst case endemic heterogeneous mixing models of HIV/AIDS

Simple models of HIV transmission assume random (proportionate) mixing among subpopulations with differing sexual activity rates, while more complex models assume some form of nonrandom heterogeneous mixing. Since the modeled number of persons infected with HIV does depend upon the specific mixing assumptions employed, it is natural to consider the maximum number of infections that could occur under any feasible mixing pattern. Such worst case results are of special interest to decision makers who must prospectively evaluate the consequences of planned public health interventions. This paper derives upper bounds for the maximum number of infected persons possible under endemic steady state conditions within the workings of a heterogeneous mixing model of HIV transmission. We present two examples that utilize this bound for a range of parameter values reasonably descriptive of HIV/AIDS. These examples, summarized in Figures 4 and 5, show that the worst case number of infected persons in the endemic steady state can be well within 10% of the number of infected persons that would result from random mixing.