Mean-max bounds for worst-case endemic mixing models

Recently developed models of HIV/AIDS demonstrate how epidemic trajectories and endemic levels of infection depend upon difficult to observe mixing patterns among population subgroups. Kaplan and Lee produced bounds for worst-case endemic mixing models without requiring knowledge of the underlying mixing patterns. This paper reduces the data requirements for bounding worst-case endemic mixing models even further. Specifically, given knowledge of the natural mortality rate, the mean incubation rate for AIDS, the average infectivity, and the mean and maximum contact rates over the entire population (hence the name mean-max), extremely simple upper and lower bounds for the maximum endemic prevalence possible owing to unobservable mixing patterns are derived and demonstrated.