Recently, there has been much debate about the prospects of eliminating HIV from high endemic countries by a test-and-treat strategy. This strategy entails regular HIV testing in the entire population and starting antiretroviral treatment immediately in all who are found to be HIV infected. We present the concept of the elimination threshold and investigate under what conditions of treatment uptake and dropout elimination of HIV is feasible. We used a deterministic model incorporating an accurate description of disease progression and variable infectivity. We derived explicit expressions for the basic reproduction number and the elimination threshold. Using estimates of exponential growth rates of HIV during the initial phase of epidemics, we investigated for which populations elimination is within reach. The concept of the elimination threshold allows an assessment of the prospects of elimination of HIV from information in the early phase of the epidemic. The relative elimination threshold quantifies prospects of elimination independently of the details of the transmission dynamics. Elimination of HIV by test-and-treat is only feasible for populations with very low reproduction numbers or if the reproduction number is lowered significantly as a result of additional interventions. Allowing low infectiousness during primary infection, the likelihood of elimination becomes somewhat higher. The elimination threshold is a powerful tool for assessing prospects of elimination from available data on epidemic growth rates of HIV. Empirical estimates of the epidemic growth rate from phylogenetic studies were used to assess the potential for elimination in specific populations.
Keywords: HIV elimination; mathematical model; primary HIV infection; treatment coverage.