Appendix

For four Sub-Saharan African countries (Ghana, Lesotho, Malawi, and Rwanda) we use mathematical modeling and empirical data to estimate the effect of treating discordant couples on: (i) the annual HIV incidence rate and (ii) the annual number of infections prevented (IP).

All of the models’ parameters are defined in Table S1; this Table also includes the parameter values used to predict the impact of an intervention based on treating discordant couples to prevent transmission in Ghana, Lesotho, Malawi, and Rwanda.

(i) Estimating the effect of treating discordant couples on the annual HIV incidence rate

To estimate the reduction in the incidence rate due to treating discordant couples to prevent transmission, we first estimated the overall incidence rate; i.e., the number of new infections occurring in both stable couples and in short-term partnerships. We used the model of Coburn et al.S1 to make estimates for Ghana, Lesotho, Malawi, and Rwanda.

  1. For stable discordant couples their incidence rate () is determined by the equation: , where represents the proportion of stable couples that are discordant and represents the probability of HIV transmission within a discordant couple. The parameter is estimated using data from EwayoS2 (Table S2). The parameter is estimated using the relationship, where represents the per act transmission probability and represents the per capita annual number of sex acts. We set to be 0.10, assuming is 0.001 and is 104.
  2. For individuals in short-term partnerships their incidence rate () is determined by the equation:. The parameter represents the prevalence of HIV in individuals who have short-term partnerships; consequently () represents the proportion of uninfected individuals that are in short-term partnerships. The parameter represents the probability of transmission within a short-term partnership and is estimated using the relationship . We use the same parameter values as for stable couples for and ; i.e., = 0.001 and = 104. To estimate the value of we used dataS3 on country-level prevalence () and the equation: , where represents the proportion of the population that is in stable couples and represents the prevalence of HIV in stable couples. HIV prevalence in stable couples is given by the equation: ; which we calculated using data from EwayoS2. We specified values for of 0.4 and 0.7 by assuming that 40% or 70%, respectively, of the population are in stable couples.
  3. We then estimated (for each of the four countries) the annual HIV incidence rate () using the expression: . This expression reflects the annual incidence rate as a weighted average of the incidence rate in stable couples and the incidence rate in short-term partnerships; the weight is the proportion of individuals in these two groups (i.e., and , respectively).

We then derived an expression for the annual HIV incidence rate ()that includes the effect of an intervention based on treating discordant couples to prevent transmission:

.

where represents treatment coverage (i.e., proportion of discordant couples that receive ART to prevent transmission), and represents the protective efficacy of treatment in protecting against HIV infection. To make our calculations we set to be 0.96 (as in the HPTN 052S4 Study) and varied treatment coverage from 0% to 100%; results shown in Table S3.

(ii) Estimating the number of IP by treating discordant couples to prevent transmission

To estimate the annual number of IP, we first estimated the annual number of infections that occur per year due to transmission in discordant couples. We made these estimates forGhana, Lesotho, Malawi, and Rwanda by:

  1. Calculating, using demographic data from the World Health OrganizationS5 and from the Measure Demographic and Health SurveysS6 (data are shown in Table 1 in the main text), the number of individuals in each of the four countries that are between 15-49 years old.
  2. Determining the number of individuals that are in couples, by assuming that between 40% to 70% of the population (aged 15-49 years old) is in stable couples.
  3. Using data for Ghana, Lesotho, Malawi, and Rwanda from Ewayo et al.S2, we classified couples into three groups based on their HIV serostatus: concordant negative, concordant positive or serodiscordant. We denote these three groups by , , and , respectively. Results are shown in Table 1 in the main text (in terms of numbers of individuals), and as percentages in Table S2.
  4. Estimating the probability of HIV transmission within a discordant couple () using the relationship, where represents the per act transmission probability and is the per capita annual number of sex acts. We estimate to be 0.10, assuming is 0.001 and is 104.
  5. Estimating the annual number of infections that occur per year due to transmission in discordant couples by multiplying by the number of uninfected individuals in discordant couples. Note, the number of uninfected individuals in serodiscordant couples is half of the population in these partnerships.

We determined the number of infections prevented from a discordant couples treatment intervention by multiplying the total number of infections in discordant couples by . To make our calculations, we set to be 0.96 and vary treatment coverage from 0% to 100%; results are shown in Table S4.

References

S1. Coburn BJ, Gerberry DJ, Blower S. Quantification of the role of discordant couples in driving incidence of HIV in sub-Saharan Africa. Lancet Infect Dis 2011;11:263-4.

S2. Eyawo O, Walque Dd, Ford N, Gakii G, Lester RT, Mills EJ. HIV status in discordant couples in sub-Saharan Africa: a systematic review and meta-analysis. The Lancet Infectious Diseases 2010;10:770-7.

S3. The World Bank. World Development Indicators. 2009. (Accessed January, 24 2011, at

S4. NIH News: Treating HIV-infected People with Antiretrovirals Protects Partners from Infection. (Accessed May 12, 2011, at http://www.niaid.nih.gov/news/newsreleases/2011/Pages/HPTN052.aspx)

S5. The World Health Organization (WHO). Country Profiles., 2011. (Accessed May 29, 2011, at

S6. Measure Household and Demographic Surveys. Calverton, MD. Measure DHS. ICF Macro, 2011. (Accessed at

Table S1. Model parameters: descriptions and values. The upper panel shows a list of the symbol and description for each of the models’ parameters. The lower panel provides the parameter valuesused for Lesotho, Malawi, Rwanda and Ghana.

Table S2. Percent of couples classified by serostatus for Lesotho, Malawi, Rwanda and Ghana. The percentages were determine from demographic and health surveysS6. The table is based on data presented by Eyawo et al.S2

Table S3. The effect of an intervention based on treating discordant couples to prevent infection as a function of treatment coverage. The upper panel shows the annual incidence that would occur in the presence of an intervention. The lower panel shows the percentage reduction in the incidence that would occur in the presence of an intervention. Calculations are based on the assumption that 40% (shown by the lower end of the range) or 70% (shown by the upper end of the range) of the population is in stable partnerships; stable partnerships include concordant positive, concordant negative and discordant couples.

Table S4. Total number of infections prevented per year due to treating discordant couples to prevent infection.Calculations are based on the assumption that 40% (shown by the lower end of the range) or 70% (shown by the upper end of the range) of the population is in stable partnerships; stable partnerships include concordant positive, concordant negative and discordant couples.

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