Reducing HIV Transmission Risk by Increasing Serostatus Disclosure: A Mathematical Modeling Analysis

Abstract

Persons living with HIV infection are encouraged to disclose their HIV-positive serostatus to prospective sex partners to decrease the likelihood of unsafe sex and HIV transmission. However, the effectiveness of serostatus disclosure as a preventive measure is not known. We developed a mathematical framework for assessing the HIV transmission risk reduction effectiveness of serostatus disclosure, examined how increasing the disclosure rate affects the transmission risk reduction effectiveness of disclosure, and explored the interaction between condom use and disclosure effectiveness. Under base-case assumptions, serostatus disclosure reduced the risk of HIV transmission by between 17.9% and 40.6% relative to no disclosure. Increasing the disclosure rate from the base-case value of 51.9–75.7% produced a 26.2–59.2% reduction in risk. The findings of this modeling study strongly support intervention efforts to increase both serostatus disclosure and condom use by persons living with HIV.

Appendix

Let D denote the likelihood that an HIV-positive person discloses his or her serostatus to a prospective sex partner, S the probability that the partner agrees to intercourse, K the probability that a condom is used for intercourse following serostatus disclosure, and C the probability of condom use in the absence of disclosure. The overall probability of HIV transmission is

$$\hbox{P(D,K,C)}\,=\,\hbox{DS}(1-\varepsilon\hbox{K})\alpha+(1-\hbox{D})(1-\varepsilon\rm{C}),$$

where α denotes the probability of HIV transmission for unprotected intercourse and ε represents the effectiveness of condoms at preventing HIV transmission. P(D,K,C) also can be written as

$$\hbox{P(D,K,C)}\,=\,(1-\hbox{E(K,C)}\,\times\,\hbox{D})(1-\varepsilon\hbox{C}),$$

where $\hbox{E(K,C)}\,=\,1-\hbox{S}(1-\varepsilon\hbox{K})/(1-\varepsilon\hbox{C})$ is the risk reduction effectiveness of serostatus disclosure.

Increasing the disclosure rate from a baseline level D ₀ to a higher level D ₁ reduces HIV transmission risk by the following proportion:

$$\begin{aligned} \frac{\hbox{P}(\hbox{D}_0\hbox{,K,C})-\hbox{P} (\hbox{D}_1\hbox{,K,C})}{\hbox{P}(\hbox{D}_0\hbox{,K,C})} &\,= \,\frac{(1-\hbox{E(K,C)}\,\times\,\hbox{D}_0)(1-\varepsilon\hbox{C})- (1-\hbox{E(K,C)}\,\times\,\hbox{D}_1)(1-\varepsilon\hbox{C})} {(1-\hbox{E(K,C)}\,\times\,\hbox{D}_0)(1-\varepsilon\hbox{C})} \\ &\,=\,(\hbox{D}_1-\hbox{D}_0)\,\times\, \frac{\hbox{E(K,C)}}{1-\hbox{E(K,C)}\,\times\,\hbox{D}_0} \\ \end{aligned}$$

The derivative of this expression with respect to E(K,C) equals (D ₁ − D ₀) / (1 − E(K,C) × D ₀)², which is greater than zero. It follows that the greater the effectiveness of disclosure, E(K,C), the larger the proportionate risk reduction produced by increasing the disclosure rate from D ₀ to D ₁. Notice in particular that increasing the disclosure rate from D ₀ = 0 (no disclosure) to D ₁ reduces HIV transmission risk by 100 × E(K,C) × D ₁%.

The HIV transmission risks associated with the two condom use rate combinations 〈K ₀,C ₀〉  and 〈K ₁,C ₁〉  are equal if and only if DS(1 − εK ₀)α + (1 − D)(1 − εC ₀)α = DS(1 − εK ₁)α + (1 − D)(1 − εC ₁)α, or equivalently, DS(K ₁ − K ₀) + (1 − D)(C ₁ − C ₀) = 0. Thus, there are an infinite number of post-disclosure/non-disclosure condom use rate combinations that produce any particular risk reduction target (up to the maximum reduction that can be achieved through consistent condom use). Some of these combinations increase the effectiveness of serostatus disclosure, and some of them decrease it. Specifically, serostatus disclosure is more effective for the condom use rate combination 〈 K ₁,C ₁ 〉  than for 〈 K ₀,C ₀ 〉  (i.e. , E(K ₁,C ₁) > E(K ₀,C ₀)) if and only if 1 − S (1 − εK ₁) / (1 − εC ₁) > 1 − S (1 − εK ₀) / (1 − εC ₀), or equivalently, (K ₁ − K ₀) − (C ₁ − C ₀) > ε(K ₁ C ₀ − K ₀ C ₁).

By itself, increasing the disclosure rate from D ₀ to D ₁ reduces HIV transmission risk by Δ _D  = P(D ₀,K ₀,C ₀) − P(D ₁,K ₀,C ₀), whereas increasing the condom use rates from K ₀ to K ₁ and from C ₀ to C ₁ produces an independent reduction in risk, Δ _C  = P(D ₀,K ₀,C ₀) − P(D ₀,K ₁,C ₁). The overall reduction in HIV transmission risk obtained by simultaneously increasing the disclosure and condom use rates, Δ = P(D ₀,K ₀,C ₀) − P(D ₁,K ₁,C ₁), equals the sum of the independent risk reductions due to increasing disclosure and increasing condom use, as well as an interaction term, x = Δ − Δ _D  − Δ _C . The interaction term is positive––indicating that the overall reduction in risk is greater than the sum of the independent reductions in risk due to increasing disclosure and condom use––if and only if the “agree to sex” rate exceeds (C ₁ − C ₀) / (K ₁ − K ₀). (Proof: The interaction term can be written x = (D ₁ − D ₀) × [E(K ₁,C ₁)(1 − εC ₁) − E(K ₀,C ₀)(1 − εC ₀)]. The desired result follows from basic arithmetic and the definition, E(K,C) = 1 − S (1 − εK) / (1 − εC). In particular, a positive interaction is possible only when the condom use changes enhance the effectiveness of serostatus disclosure (i.e., E(K ₁,C ₁) > E(K ₀,C ₀)). (Proof: S > (C ₁ − C ₀) / (K ₁ − K ₀) = > (S − εSK ₀) − (S − εSK ₁) > (1 − εC ₀) − (1 − εC ₁) = > E(K ₁,C ₁)(1 − εC ₁) > E(K ₀,C ₀)(1 − εC ₀) = > E(K ₁,C ₁) > E(K ₀,C ₀) since C ₁ > C ₀.)

For convenience, the main analyses assume that sexual relationships consist of a single act of intercourse. To model multiple-act relationships, let R _D denote the probability of transmission if the HIV-positive person discloses his or her serostatus and R _N denote the transmission probability if he or she does not. (For a single act of intercourse, R _N  = 1 − εC and R _D  = S (1 − εK).) Define the risk reduction effectiveness of serostatus disclosure to be the proportionate risk reduction, E = (R _N  − R _D ) / R _N . The main analytic findings hold for this more general definition of disclosure effectiveness (cf. Table 1).