Prospects of elimination of HIV with test-and-treat strategy

Abstract

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.

Fig. 1.

Flowscheme of the model.

Fig. 2.

(A) Probability of being in a specific stage of infection as a function of time since infection (red: primary infection; green: chronic asymptomatic stage; blue: AIDS mild; magenta: AIDS severe); mean durations are stage 1: 0.271 y; stage 2: 8.31 y; stage 3: 1.18 y; stage 4: 1.32 y. (B) Infectivity of the different stages of infection. Stage 1 (red): 2.76/y; stage 2 (green): 0.106/y; stage 3 (blue): 0.64/y; stage 4 (magenta): 0.0/y. (C) Generation time distribution (blue shaded area) and cumulative fraction of secondary infections (red curve) as a function of time since infection.

Fig. 3.

(A) Relationship between epidemic growth rate and R₀. (B) Relationship between epidemic doubling time and R₀.

Fig. 4.

(A) Elimination threshold R_e as a function of annual treatment uptake and dropout rate for a population with an epidemic growth rate r of 0.273/y. (B) Relative threshold quantity R_f as a function of annual treatment uptake (blue) and dropout rate (red). The respective other parameter is kept constant: the blue curve assumes a dropout rate of 5%; the red curve assumes annual treatment uptake of 80%. Horizontal lines show where the elimination threshold is reached for different values of the exponential growth rate. The uppermost line denotes the threshold for r = 0.273, the lines below for multiples of that value. (C) Relationship between annual treatment uptake and the coverage at a steady state for different values of the dropout rate.

Fig. 5.

Impact of distribution of infectivity during the infectious period on the elimination threshold. The infectivity distribution from Fig. 2B leads to the upper red curve. Then infectivity is shifted stepwise from primary to chronic infection while retaining a constant total infectivity (coloring of curves shifting from red to green). With infectivity shifting to later stages of infection the required annual treatment uptake for elimination (dots) decreases. The epidemic growth rate is again set to 0.273/y and dropout rate is assumed to be 5% per year.

Fig. 6.

(A) Elimination threshold as function of annual treatment uptake and dropout rate for various values of the basic reproduction number R₀. The two curves describe the threshold for R₀ = 2.0 and R₀ = 3.0. For parameter combinations above the lines, elimination is possible; for combinations below the curve it is not possible. (B) Elimination threshold in a heterogeneous population, where partner change rates declined between onset of the epidemic and start of prevention test-and-treat intervention. The epidemic growth rate at onset of the epidemic is 0.273/y. Elimination thresholds are shown as function of annual treatment uptake and dropout rate for various reduction percentages of the partner change rates of the high-risk population. For parameter combinations above the lines, elimination is possible; for combinations below the curve it is not possible.