Strong influence of behavioral dynamics on the ability of testing and treating HIV to stop transmission

Abstract

Choosing between strategies to control HIV transmission with antivirals requires understanding both the dynamics affecting those strategies' effectiveness and what causes those dynamics. Alternating episodes of high and low contact rates (episodic risk) interact with increased transmission probabilities during early infection to strongly influence HIV transmission dynamics. To elucidate the mechanics of this interaction and how these alter the effectiveness of universal test and treat (UT8T) strategies, we formulated a model of UT8T effects. Analysis of this model shows how and why changing the dynamics of episodic risk changes the fraction of early transmissions (FET) and the basic reproduction number (R0) and consequently causes UT8T to vary from easily eliminating transmission to having little effect. As the length of risk episodes varies from days to lifetimes, FET first increases, then falls. Endemic prevalence varies similarly. R0, in contrast, increases monotonically and is the major determinant of UT8T effects. At some levels of episodic risk, FET can be high, but eradication is easy because R0 is low. At others FET is lower, but a high R0 makes eradication impossible and control ineffective. Thus changes in individual risk over time must be measured and analyzed to plan effective control strategies with antivirals.

Figure 1. Heatmaps plotting (a) the basic reproduction number (R₀), and (b) equilibrium prevalence (P) against the relative transmissibility during early HIV infection (ζ) and re-selection rate (ω).

The per-act transmissibilities during EHI and chronic infection for each parameter set were chosen based on the constraints that (1) their ratio must be ζ and (2) the total transmission potential in a homogeneous system must be the same for all parameter sets. This transmission potential was chosen by setting the endemic prevalence for the lower-left parameter set to be 0.2. The other parameters used are summarized in Supplementary Table 1 in §2 of the Supplementary Information. Each panel has a scale that runs from the lowest to the highest value observed in that panel.

Figure 2. Heatmaps plotting (a) the effective treatment rate required to achieve elimination (τ_E), (b) the basic reproduction number (R₀), and (c) the fraction of transmissions from early HIV infection (φ) against the relative transmissibility during early HIV infection (ζ) and re-selection rate (ω).

The other parameters used are summarized in Supplementary Table 1 in §2 of the Supplementary Information. Each panel has a scale that runs from the lowest to the highest value observed in that panel.

Figure 3. Curves showing the prevalence as a function of R₀ when all parameters except the overall transmissibility are held constant.

The curves shown are for the full (maximal) model (episodic risk, with assortative mixing (m = 0.5) – EA), and several reduced models: Episodic risk, with proportional mixing (EP, the primary model in this paper); Static risk heterogeneity, with assortative mixing (m = 0.5) (SA); Static risk heterogeneity, with proportional mixing (SP), and Behavioral Homogeneity (BH). The formulation of these reduced models is discussed in more detail in §3.5 of the Supplementary Methods. The dashed black line indicates a constant prevalence of 0.2, illustrating the drastically different values of R₀ that are possible when the prevalence is fixed.

Figure 4. The basic reproduction number (R₀) and effective treatment rate required to achieve elimination (τ_E) as a function of the re-selection rate (ω).

The prevalence is fixed at 0.2, and the fraction of transmissions from EHI (φ) is fixed at 0.447. To achieve this, the transmissibilities from each of acute and chronic infection are allowed to vary; all other parameters are fixed. Details are presented in §3.7 of the Supplementary Methods.

Figure 5. Dynamics of acquisition, progression, and treatment of infection.

The meanings of symbols representing subpopulations are given in Table 1, and the meanings of symbols representing parameters (including derived parameters) are given in Table 2. Note that only re-selections resulting in transition to the other risk group are shown; loops depicting re-selections that place the individual in the same risk group (and therefore same compartment) they were in prior to re-selection are not included.