Test-and-treat approach to HIV/AIDS: a primer for mathematical modeling

Abstract

The public benefit of test-and-treat has induced a need to justify goodness for the public, and mathematical modeling studies have played a key role in designing and evaluating the test-and-treat strategy for controlling HIV/AIDS. Here we briefly and comprehensively review the essence of contemporary understanding of the test-and-treat policy through mathematical modeling approaches and identify key pitfalls that have been identified to date. While the decrease in HIV incidence is achieved with certain coverages of diagnosis, care and continued treatment, HIV prevalence is not necessarily decreased and sometimes the test-and-treat is accompanied by increased long-term cost of antiretroviral therapy (ART). To confront with the complexity of assessment on this policy, the elimination threshold or the effective reproduction number has been proposed for its use in determining the overall success to anticipate the eventual elimination. Since the publication of original model in 2009, key issues of test-and-treat modeling studies have been identified, including theoretical problems surrounding the sexual partnership network, heterogeneities in the transmission dynamics, and realistic issues of achieving and maintaining high treatment coverage in the most hard-to-reach populations. To explicitly design country-specific control policy, quantitative modeling approaches to each single setting with differing epidemiological context would require multi-disciplinary collaborations among clinicians, public health practitioners, laboratory technologists, epidemiologists and mathematical modelers.

Fig. 1

Flow chart of a simple compartmental model. Variable H _u [H _d] is a fraction of undiagnosed [diagnosed] HIV-infected individuals without AIDS, A _u [A _d] is a fraction of previously undiagnosed [diagnosed] AIDS cases

Fig. 2

HIV care continuum in the United States, 2011. Estimated percentages of persons living with HIV infection are shown [11]. In 2011, an estimated 1.2 million persons were living with HIV infection in the United States

Fig. 3

Test-and-treat with high screening rate may lead to the elimination of HIV. When the rate of diagnosis is greater than a certain threshold value, test-and-treat can successfully control HIV epidemic. Parameter values are μ = 1/60, ρ = 1/10, γ = 1/3, β = 0.15, δ = 1/2 and ε = 0.3

Fig. 4

Test-and-treat could increase HIV prevalence. a, c The rate of change in HIV incidence, (b, d) the proportion of the PLWHA (people living with HIV/AIDS). Without test-and-treat policy, the rate of diagnosis was set as α = 0. Under the test-and-treat policy, α = 0.3 was adopted. Parameter values are μ = 1/60, ρ = 1/10, γ = 1/3, β = 0.15, δ = 1/2 and ε = 0.3. The test-and-treat reduces both the incidence and the prevalence in (a) and (b). For panel (c) and (d), ε = 0.5 was used instead of ε = 0.3 as the relative transmissibility for those who are diagnosed. In this scenario, test-and-treat increases HIV prevalence. Initial values are H _u = 0.15, A _u = 0.01, H _d = 0 and A _d = 0