The impact of mixing on endemic prevalence in the model without treatment.

<p>(A) Total prevalence in the population. The color of the bars corresponds to the variance in the rate of partner change, <i>σ</i>². Note that prevalence is zero for the parameters where HIV is not able to spread (yellow curves for all levels of mixing and the green curve for proportionate mixing in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005012#pcbi.1005012.g003" target="_blank">Fig 3</a>). (B) Prevalence per risk group for a population with a variance in the rate of partner change <i>σ</i>² of 32.6 yr⁻² corresponding to the data. The color of the bars denotes the number of the sexual activity class.</p

Impact of Heterogeneity in Sexual Behavior on Effectiveness in Reducing HIV Transmission with Test-and-Treat Strategy

<div><p>The WHO’s early-release guideline for antiretroviral treatment (ART) of HIV infection based on a recent trial conducted in 34 countries recommends starting treatment immediately upon an HIV diagnosis. Therefore, the test-and-treat strategy may become more widely used in an effort to scale up HIV treatment and curb further transmission. Here we examine behavioural determinants of HIV transmission and how heterogeneity in sexual behaviour influences the outcomes of this strategy. Using a deterministic model, we perform a systematic investigation into the effects of various mixing patterns in a population of men who have sex with men (MSM), stratified by partner change rates, on the elimination threshold and endemic HIV prevalence. We find that both the level of overdispersion in the distribution of the number of sexual partners and mixing between population subgroups have a large influence on endemic prevalence before introduction of ART and on possible long term effectiveness of ART. Increasing heterogeneity in risk behavior may lead to lower endemic prevalence levels, but requires higher coverage levels of ART for elimination. Elimination is only feasible for populations with a rather low degree of assortativeness of mixing and requires treatment coverage of almost 80% if rates of testing and treatment uptake by all population subgroups are equal. In this case, for fully assortative mixing and 80% coverage endemic prevalence is reduced by 57%. In the presence of heterogeneity in ART uptake, elimination is easier to achieve when the subpopulation with highest risk behavior is tested and treated more often than the rest of the population, and vice versa when it is less. The developed framework can be used to extract information on behavioral heterogeneity from existing data which is otherwise hard to determine from population surveys.</p></div

Effective reproduction number and treatment coverage for different annual treatment uptakes and dropout percentages.

<p>(A) The impact of annual treatment uptake, <i>τ</i>*, on the effective reproduction number for a population with the variance in the rate of partner change corresponding to the data. Mixing is proportionate (assortative) for <i>ω</i> = 1 (<i>ω</i> = 0). The curve plotted for <i>τ</i>* = 0.0 is, by definition, <i>R</i>₀. The dashed line indicates the threshold value of <i>R</i>_<i>e</i> = 1 below which HIV is eliminated from the population. <i>R</i>_<i>e</i> decreases with increasing treatment uptake and mixing. (B) Treatment coverage as a function of annual treatment uptake <i>τ</i>* for different dropout percentages <i>ϕ</i>* and the remaining parameters as in A.</p

Schematic diagram of the HIV model.

<p>The model describes HIV infection process, disease progression through <i>n</i> stages of infection, birth, background mortality and HIV related mortality, the uptake of and dropping out of ART. The model assumes that the population is divided into the classes of susceptibles, <i>S</i>_<i>l</i>(<i>t</i>), infected, <i>I</i>_<i>lk</i>(<i>t</i>), and treated, <i>A</i>_<i>lk</i>(<i>t</i>), in <i>n</i> stages of infection, <i>k</i> = 1, …, <i>n</i>. The population is stratified into <i>m</i> risk groups indicated by the label <i>l</i> = 1, …, <i>m</i> in the subscript, and the diagram describes the dynamics in one of them. The risk groups differ only in their partner change rates and initial group sizes, whilst the disease progression and dropping out of treatment are the same for all risk groups. The diagram shows the situation when treatment uptake is the same by all risk groups. We denote <i>τ</i>_<i>l</i> the uptake by risk group <i>l</i> when we consider heterogeneous ART uptake by risk group. The interaction between the groups is encoded in the time-dependent force of infection <i>J</i>_<i>l</i>(<i>t</i>) that takes into account mixing between the risk groups.</p

Distributions in the partner change rate used in the analysis have the same mean rate estimated from the data and different variances.

<p>(A) Probability density function for the Weibull distribution in the partner change rate fitted to the WPF data histogram by maximum likelihood method. The dashed lines indicate the intervals defined by the initial fractions of the population in the 6 risk groups, <i>q</i>_<i>l</i>, <i>l</i> = 1, …, 6, per which mean rates of partner change were estimated. For a better visualization the ranges of the x and y axes differ among the panel A and the panel B that is why not all dashed lines can be seen, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005012#pcbi.1005012.s004" target="_blank">S3 Fig</a> for more detail. (B) Weibull distributions with the same mean of <i>c</i> = 2.54 partners per year and different variances, <i>σ</i>², were obtained by varying the shape parameter, <i>α</i>, and the scale parameter, <i>β</i>. The Weibull distribution that best fits to the data is shown in black.</p

Effective reproduction number for heterogeneous uptake of testing and treatment.

<p> denotes the uptake by risk group <i>l</i>. We considered progressively higher uptake rates by groups with higher numbers of partners. Specifically, we assumed that (lowest risk group), (highest risk group), and uptakes by the remaining 4 groups were equally spaced and increasing from 26% to 74%. The dashed line is <i>R</i>₀ before ART. Also shown is <i>R</i>_<i>e</i> for a constant treatment uptake rate of 23.25% computed as an average of uptakes by different groups weighted by their population size, . Heterogeneous test-and-treat with increasing treatment uptakes by higher risk groups has a larger impact on <i>R</i>_<i>e</i> than homogeneous test-and-treat with a constant average uptake. See also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005012#pcbi.1005012.s008" target="_blank">S7 Fig</a> with results for other combinations of treatment uptakes by different risk groups.</p

The impact of mixing on the basic reproduction number in the model without treatment.

<p>The results are for populations with different variances in partner change rates, <i>σ</i>², and the mean rate of partner change kept constant. Mixing is proportionate (assortative) for <i>ω</i> = 1 (<i>ω</i> = 0). The dashed line indicates the threshold value of <i>R</i>₀ = 1 below which HIV cannot spread in the population. <i>R</i>₀ decreases as the mixing becomes proportionate and the variance gets lower. For low variances and high levels of mixing (i.e. low levels of assortativeness) <i>R</i>₀ can be smaller than 1 even in the absence of treatment. For the lowest variance we used in the analysis HIV cannot persist for any level of mixing (the yellow curve).</p

Lorenz curves in the model without treatment.

<p>The results are for populations with different variances in partner change rates, <i>σ</i>², and the mean rate of partner change kept constant. The diagonal line represents the situation in which every risk group would have the same HIV prevalence. Lorenz curves deviate from it which means that the distributions of infection across the risk groups for proportionate, intermediate and assortative mixing are skewed with high prevalence in small high risk groups. This effect gets stronger as the mixing becomes more assortative. Note that we did not plot the results for the parameters used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005012#pcbi.1005012.g003" target="_blank">Fig 3</a> for which HIV is not able to spread (yellow curves for all levels of mixing and the green curve for proportionate mixing).</p

Effective reproduction number as a function of mixing and treatment uptake with and without uptake during the primary infection.

<p>The solid lines are repeated from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005012#pcbi.1005012.g006" target="_blank">Fig 6A</a> and correspond to the annual treatment uptake percentage, <i>τ</i>*. The dashed lines were obtained when treatment uptake during the primary infection was set to 0 for all risk groups. As expected, elimination is more difficult to achieve in this case and the impact of not treating primary infection increases with increasing treatment uptake.</p

Percentage reduction in the total prevalence due to treatment.

<p>The variance in the rate of partner change equals that of the data. The color of the bars corresponds to the annual treatment uptake, <i>τ</i>*.</p