Our gender-stratified estimates of HIV incidence rates and prevalence levels, obtained from the calibration procedure (see Methods), show significant geographic variation throughout South Africa. Province-specific gender-stratified estimates of HIV incidence rates, in terms of the median value and Inter-Quartile-Range (IQR), are given in Supplementary Table 2. Province-specific gender-stratified estimates of both HIV and HSV-2 prevalence levels are shown in Supplementary Fig. 2.

The results of the multivariate sensitivity analysis of the geospatial MT model are presented as three-dimensional response hypersurfaces (Fig. 1); the colors in the hypersurfaces show the percent reduction in transmission in KwaZulu-Natal, due to microbicides, over a decade. Fig. 1 shows the impact of microbicides as a function of their effectiveness in protecting against HIV infection (Y-axis) and the coverage of the intervention (X-axis). Fig. 1A shows the reduction in HIV transmission for women, and Fig. 1B the reduction in HIV transmission for men. Fig. 1C shows the reduction in HSV-2 transmission for women, and Fig. 1D the reduction in HSV-2 transmission for men. The response hypersurfaces show that, over a decade, the maximum reduction in HIV transmission in women could be as high as ~60%; however this would only be possible if the effectiveness of the microbicide was high (~70%) and coverage reached ~90% (Fig. 1A). Under these conditions, HSV-2 transmission in women would be reduced by ~30% (Fig. 1C). Men would also benefit from microbicides, but to a lesser extent; their HIV transmission would be reduced by a maximum of 25% over a decade (Fig. 1B) and their HSV-2 transmission by a maximum of 10% (Fig. 1D). The reduction in HSV-2 transmission depends on microbicide coverage, but does not increase with an increase in effectiveness (over the range from 15% to 75%) of the microbicide against HIV (Fig. 1C and 1D).

The results from the scenario analyses show the effect of microbicide-based interventions in KwaZulu-Natal on reducing both HIV transmission (Fig. 2A for women, Fig. 2B for men) and HSV-2 transmission (Fig. 2C for women, Fig. 2D for men). Coverage is 90% in scenarios shown as solid lines and 60% in scenarios shown as dotted lines. Red, green and blue lines represent scenarios where adherence is low (red), moderate (green) or high (blue); the corresponding effectiveness of the microbicide against HIV infection is 28%, 38%, and 54%. In all scenarios, regardless of adherence, the effectiveness of the microbicide against HSV-2 infection is 51%. See Methods for the definitions of adherence and effectiveness, and their relation to data from the CAPRISA 004 trial.

The percentage of HIV IP in women increases quickly for ~3 years; it then continues to increase but at a slower rate (Fig. 2A). The greater the effectiveness of the microbicide against HIV and/or the higher the coverage the more HIV infections are prevented (Fig. 2A). The percentage of HIV IP in men continues to steadily increase over a decade, but is always significantly lower than in women (Fig. 2B). Reduction in HIV transmission in men is a delayed effect because of the indirect benefit of microbicides. The percent reduction in HSV-2 transmission in women increases quickly for 2–3 years, but then plateaus (Fig. 2C). The higher the coverage, the more HSV-2 IP; however the degree of effectiveness against HIV (over the range: ~15% to ~75%) has virtually no effect on the number of HSV-2 IP (Figs 2C and 2D). The percentage of HSV-2 IP in men continues to steadily increase over a decade, but is always significantly lower than in women (Fig. 2D).

The effect of the HSV-2 epidemic on increasing HIV transmission in South Africa is due to the high prevalence of HSV-2 (~60% in women and ~40% in men), and a reduction in HSV-2 transmission would not lead to a reduction in HSV-2 prevalence for several decades. Consequently, the additional “benefit” of the CAPRISA microbicide (i.e., the effect of the microbicide in partially protecting against HSV-2 infection) will not substantially increase its impact on reducing HIV transmission over the time period of our analyses (i.e. over a decade).

The cumulative number of HIV IP in each province, over a decade, is shown in Fig. 3; the predictions are based on assuming a high coverage (~90%) of the intervention. Predictions that are based on assuming moderate coverage (~60%) are shown in Supplementary Fig. 3. The predictive maps in Fig. 3 and Supplementary Fig. 3 show median values calculated from uncertainty analyses; see Methods. Figs 3A for women and 3B for men are based on assuming a high level of adherence. Figs 3C for women and 3D for men are based on assuming a moderate level of adherence. Both coverage and adherence determine the absolute number of HIV IP (Fig. 3 and Supplementary Fig. 3): the greater the coverage and/or the higher the adherence the more HIV IP. The histograms in the prediction maps show the gender-stratified prevalence of HIV in each province at the beginning of the rollout: prevalence in women (pink) and in men (blue). For comparison, histograms are scaled to the same degree in each province: province-specific prevalence levels are given in Supplementary Table 1.

Aggregating the results over all nine provinces, we predict that the total number of HIV IP over a decade in South Africa due to microbicide-based interventions would be: 580,000 (median: IQR 500,000 to 670,000) in women and 190,000 (median: IQR 160,000 to 230,000) in men if adherence and coverage are high; 410,000 (median: IQR 340,000 to 490,000) in women and 136,000 (median: IQR 110,000 to 170,000) in men if adherence is moderate and coverage is high; 360,000 (median: IQR 310,000 to 420,000) in women and 110,000 (median: IQR 93,000 to 140,000) in men if adherence is high and coverage is moderate; 260,000 (median: IQR 210,000 to 300,000) in women and 81,000 (median: IQR 65,000 to 100,000) in men if both adherence and coverage are moderate.

The long-term efficiency of interventions in reducing HIV transmission shows substantial geographic variation throughout South Africa (Fig. 4, which is based on assuming coverage is high (~90%)). Long-term efficiency is defined in terms of the number of women-years on microbicides that are needed to prevent one HIV infection in women or one HIV infection in men; efficiency increases as the number of women-years needed to prevent one HIV infection decreases. The intervention efficiency maps in Fig. 4 show median values calculated from uncertainty analyses of the geospatial MT model; see Methods. Figs 4A and 4B are based on high adherence, Figs 4C and 4D on moderate adherence; Figs 4A and 4C show intervention efficiency maps for women, Figs 4B and 4D for men. The maps show that the gender-specific intervention will reduce HIV transmission in men, as well as in women; although, not surprisingly microbicide-based interventions will be less efficient in reducing HIV transmission in men than in women. For example, in KwaZulu-Natal ~3 times more women-years are needed to prevent one HIV infection in men than to prevent one HIV infection in women. The intervention efficiency maps in Fig. 4 (based on the color-coding) show that the nine provinces can be classified into three groups based on the long-term efficiency of interventions in reducing HIV transmission in women: high long-term efficiency (KwaZulu-Natal, Mpumalanga, the Free State and the North West Province), moderate long-term efficiency (Guateng, Limpopo and the Eastern Cape) and low long-term efficiency (the Northern and Western Cape). Results are similar for men. The difference in long-term efficiency among the provinces is substantial; for example, in KwaZulu-Natal only ~110 women-years (median value) are needed to prevent one HIV infection in women whereas ~450 women-years (median value) are needed in the Western Cape (Fig. 4A).

The long-term efficiency of interventions in reducing HIV transmission decreases with adherence, Fig. 4. Notably, coverage (over the range 60% to 90%) has essentially no effect on the long-term efficiency of interventions; results shown in Fig. 4 are for high coverage (~90%) and those shown in Supplementary Fig. 4 are for moderate coverage (~60%).

We found that the pre-intervention HIV incidence rate determines the long-term efficiency of interventions in reducing HIV transmission in both women (Fig. 5) and men (Fig. 6): the higher the HIV incidence rate, the greater the long-term efficiency. Also the higher the adherence, the greater the efficiency: Figs 5A and 6A are based on high adherence, Figs 5B and 6B on moderate adherence. The long-term efficiency of interventions in reducing HIV transmission in men is substantially lower than in women, as shown by the difference in scale on the Y-axis between Figs 5 and 6. The color code for each of the nine provinces is given in the Figure Legends. Data clouds are shown as these results are generated from uncertainty analyses of the geospatial MT model; see Methods. Notably, the relationship between the pre-intervention HIV incidence rate and the long-term efficiency of interventions in preventing HIV infection in both genders is highly non-linear: efficiency increases disproportionately with increasing incidence rates. Results in Fig. 5C show the relationship between the incidence rate and the long-term efficiency of interventions when the pre-intervention HIV incidence rate is moderate to high (3–10%); again the higher the adherence, the greater the efficiency (the solid red line represents high adherence, the dotted red line moderate adherence). If adherence is high the relationship between the number of women-years needed to prevent one HIV infection, y, in women and the average pre-intervention incidence rate in women, x, can be specified by y = 1/0.00499x; see Methods. If adherence is moderate the relationship can be specified by y = 1/0.00361x. Fig. 5C shows, that under certain conditions, the long-term efficiency of interventions could be extremely high. For example, if interventions are rolled out in areas where HIV incidence rates in women are high (e.g., 10%) and adherence is high, only ~20 women-years on microbicides would be needed to prevent one HIV infection in women (Fig. 5C).

The short-term (i.e., in the first year of a rollout) efficiency of interventions in reducing HIV transmission, like the long-term efficiency (Fig. 4), shows substantial geographic variation throughout South Africa (Fig. 7A and 7B); short-term efficiency is defined in terms of the number of HIV IP per 10,000 microbicides in the first year of a rollout. The boxplots in Figs 7A and 7B show the estimates for the short-term efficiency of interventions in reducing HIV incidence rates in women in each province. These results were calculated based on uncertainty analyses of the geospatial MT model; see Methods. The variation in the estimates of short-term efficiency, shown in the boxplots, is due to the uncertainty in the estimates of the province-specific pre-intervention HIV incidence rate in women and in the province-specific estimates of the average number of new sex partners per woman per year (see Supplementary Tables 2 and 3). Adherence has only a minor effect on short-term efficiency: Fig. 7A is based on high adherence, Fig. 7B on moderate adherence. Short-term efficiency, assuming high adherence, ranges from a high of 2.55 (median: IQR 2.31 to 2.81) HIV IP in women per 10,000 microbicides in Mpumalanga to a low of 0.81 (median: IQR 0.69 to 0.92) HIV IP in women per 10,000 microbicides in the Western Cape (Fig. 7A). Notably, Mpumalanga and KwaZulu-Natal appear to be the provinces where the short-term efficiency of interventions would be the highest, and the Northern and Western Cape the provinces where the short-term efficiency would be the lowest. However, because there is considerable overlap in the within-province estimates of efficiency, the results shown in Figs 7A and 7B cannot be used to identify the province where interventions would be the most efficient in the first year of a rollout or to determine a priority ranking of provinces based on short-term efficiency.

We used a probabilistic analysis in order to identify the provinces where interventions are most likely to have the highest efficiency in reducing HIV incidence in women in the first year of a rollout. To conduct this analysis we stochastically reordered the estimates of short-term efficiency, independently for each province. Results are shown in Fig. 7C in the form of stacked histograms: rank 1 indicates the province where interventions would be the most efficient and rank 9 the province where they would be the least efficient. These results show that it is most probable that interventions would be the most efficient in two provinces (KwaZulu-Natal and Mpumalanga), but it cannot be determined whether they would be the most efficient in KwaZulu-Natal or in Mpumalanga. Furthermore, it is highly probable that the Northern and the Western Cape are the provinces where interventions are most likely to be the least efficient in the first year of a rollout (Fig. 7C). The North West province is likely to be in 6^th place and Guateng in 7^th place, but the rank ordering of Limpopo, the Eastern Cape, and the Free State in terms of 3^rd, 4^th and 5^th place is not clear (Fig. 7C). Notably the probabilistic ranking based on short-term efficiency estimates (Fig. 7C) is not exactly the same as the probabilistic ranking based on long-term efficiency estimates (Fig. 3). This is because over time (in our case, a decade) HIV incidence rates will decrease (for both genders), as a function of increased coverage of treatment and the effects of the intervention, and the long-term efficiency of interventions is a nonlinear function of the HIV incidence rate (Figs 5 and 6).

We also used a probabilistic analysis to determine the geographic regions where HIV incidence rates in women are currently the highest; to conduct this analysis we stochastically reordered the estimates for HIV incidence rates, independently for each province. These results are shown in Fig. 7D, where rank 1 indicates the province with the highest HIV incidence in women and rank 9 the province with the lowest HIV incidence. These results show that it cannot be concluded with certainty which province has the highest HIV incidence rate, but that it is most probably KwaZulu-Natal. Clearly, the Northern Cape and the Western Cape are provinces where HIV incidence is most likely to be the lowest (Fig. 7D). The ranking of the provinces based on estimates of HIV incidence rates is similar to the ranking based on estimates of the long-term efficiency of interventions. However the ranking of the provinces based on estimates of HIV incidence rates (Fig. 7D) is not exactly the same as the ranking of the provinces based on estimates of short-term efficiency (Fig. 7C). This is because short-term efficiency depends upon both HIV incidence and the levels of sexual behavior (see Methods). For example, if two provinces have the same HIV incidence rate but women in province A have (on average) slightly more partners than women in province B, interventions would be more efficient in reducing HIV transmission in province B than in province A. If the number of sex partners were exactly the same in every province (and incidence rates were known with certainty) then a ranking of the provinces based on short-term efficiency would be the same as a ranking based on HIV incidence rates.

The GRAS for implementing the utilitarian rollout plan, under different levels of resource constraints, is shown by the pie charts in Figs 8A and 8B; in both charts it is assumed that adherence is high. These results were obtained from a single optimization analysis where it was assumed that there was no uncertainty in estimating province-specific pre-intervention HIV incidence rates in women, province-specific pre-intervention HIV prevalence levels in women or province-specific levels of risk behavior (see Methods); the objective of the optimization was to maximize the number of HIV IP throughout South Africa. Results in Fig. 8A are based on assuming there are 50 million microbicides to allocate in the first year of the rollout, this is enough for 35% of the 15–49 year old HIV-negative women in South Africa. Results in Fig. 8B are based on assuming there are 100 million microbicides to allocate, this is enough for 65% of the 15–49 year old HIV-negative women in South Africa. The optimization results show that under the utilitarian plan interventions should only be allocated to two of the nine provinces: Mpumalanga and KwaZulu-Natal (Figs 8A and 8B). Therefore the optimal geographic location to rollout the utilitarian plan is in these two provinces. Mpumalanga and KwaZulu-Natal are the provinces where it is most probable that interventions would be the most efficient in reducing HIV incidence in women (Fig. 7C), and where HIV incidence in women is likely to be the highest (Fig. 7D). Similar results are obtained if adherence is moderate (Supplementary Fig. 5).

The GRAS for implementing the utilitarian rollout plan, given 50 million microbicides, is to give 56% to Mpumalanga and 44% of the supply to KwaZulu-Natal (Fig. 8A). The GRAS for implementing the utilitarian rollout plan, given 100 million microbicides, is to give 72% of the supply to KwaZulu-Natal and 28% to Mpumalanga (Fig. 8B). When only 50 million microbicides are available there are not enough microbicides to give them to all the HIV-negative women who want them in both Mpumalanga and KwaZulu-Natal. Because it is slightly more probable that interventions will be more efficient in the first year of a rollout in Mpumalanga than KwaZulu-Natal (Fig. 7C), the optimization algorithm first allocates the available resources to Mpumalanga to provide to all the women who want them and then allocates the remaining resources to KwaZulu-Natal. Consequently, under this level of resource constraint Mpumalanga receives slightly more of the available resources than KwaZulu-Natal. However when 100 million microbicides are available, Mpumalanga still receives the same number of microbicides (i.e., enough to provide to all the women who want them), but there are now many more leftover to give to KwaZulu-Natal. Consequently, under this level of resource constraint, KwaZulu-Natal receives more of the available resources than Mpumalanga.

The egalitarian plan is implemented by using a proportional GRAS; this is the conventional approach for sharing a limited supply of resources, and it results in the same coverage level in every province. Using the proportional GRAS, the proportion of the supply given to each province is equal to the number of HIV-negative women living in that province divided by the total number of HIV-negative women in South Africa. This GRAS is shown by the pie chart in Fig. 8C that shows that the resources should be shared among all nine provinces. The percentage of the supply of microbicides that should be given to each province ranges from 2% (for the Northern Cape) to 21% (for Guateng province). These results show that interventions should be rolled out, simultaneously, in all nine provinces. Notably, the GRAS for the egalitarian plan only depends upon the geographic distribution of the population of HIV-negative women in South Africa; it does not depend upon the level of resource constraints. If there were no resource constraints, the GRAS for implementing the utilitarian rollout plan would be the same as the GRAS for the egalitarian plan.

If 50 million microbicides are available and adherence is high, using the GRAS for the utilitarian plan (shown in Fig. 8A) would prevent 41% more HIV infections in South Africa in the first year of the rollout than the egalitarian plan: ~14,100 HIV IP versus ~10,000 HIV IP. If the same number of microbicides are available and adherence is moderate, using the GRAS for the utilitarian plan (shown in Supplementary Fig. 5A) would prevent ~40% more HIV infections in South Africa in the first year of the rollout than the egalitarian plan: ~12,800 HIV IP versus ~9,200 HIV IP. If 100 million microbicides are available and adherence is high, using the GRAS for the utilitarian plan (shown in Fig. 8B) would prevent ~38% more HIV infections in South Africa in the first year of the rollout than the egalitarian plan: ~27,500 HIV IP versus ~20,000 HIV IP. If the same number of microbicides are available and adherence is moderate, using the GRAS for the utilitarian plan (shown in Supplementary Fig. 5B) would prevent ~34% more HIV infections in South Africa in the first year of the rollout than the egalitarian plan: ~24,600 HIV IP versus ~18,400 HIV IP.

Results from multiple (1,362 were conducted, see Methods) optimization analyses that include uncertainty in the province-specific estimates of the pre-intervention HIV incidence rates in women, the pre-intervention HIV prevalence levels in women and the levels of risk behavior are shown in Table 1. In these analyses the rank ordering of the provinces, in terms of HIV incidence rates in women, was varied probabilistically. Each optimization analysis calculated the GRAS necessary for implementing the utilitarian plan, and identified the optimal location for initiating the rollout in terms of a combination of two provinces. It was assumed that 50 million microbicides would be available. The combinations that occurred most frequently from the multiple optimization analyses are shown in Table 1. The most frequent combination was Mpumalanga and KwaZulu-Natal; the same two provinces that were identified in the initial optimization analysis that did not include uncertainty. However, this specific combination was only found in 37% of the optimizations; this occurred because it is not certain in which of several provinces interventions would be the most efficient in reducing HIV incidence in women (Fig. 7C). Our results show it cannot be concluded with certainty that Mpumalanga and KwaZulu-Natal are the optimal combination of provinces to begin the rollout, but it should be noted that this combination occurred twice as frequently as the next most frequent two-province combination (Table 1).

In all of the optimization analyses rolling out interventions using the utilitarian plan prevented substantially more HIV infections in women in the first year of the rollout than using the egalitarian plan. However due to the uncertainty in parameter estimation, the results show fairly wide variation in terms of the allocation of resources between Mpumalanga and KwaZulu-Natal (i.e., in the GRAS necessary for implementing the utilitarian plan), Table 1. Even when Mpumalanga and KwaZulu-Natal are identified as the optimal two provinces to begin the rollout there is fairly wide variation in the GRAS. This is because in ~50% of the optimizations Mpumalanga was identified as the province where interventions would be the most efficient in the first year of the rollout in reducing HIV incidence rates in women (Fig. 7C) and was therefore allocated the largest proportion of resources, and in ~50% KwaZulu-Natal was identified as the province where short-term efficiency would be the highest (Fig. 7C) and was therefore allocated the largest proportion of resources. In addition, KwaZulu-Natal is a much larger province than Mpumalanga; consequently our results show that (given uncertainty in province-specific pre-intervention HIV incidence estimates in women, province-specific pre-intervention HIV prevalence levels in women, and province-specific levels of risk behavior), on average, slightly more resources should be allocated to KwaZulu-Natal than to Mpumalanga. In contrast the initial optimization analysis, that did not include uncertainty, could only calculate a single GRAS. Since this was based on identifying Mpumalanga as the province where interventions would be most efficient, the GRAS was to allocate slightly more of the resources to Mpumalanga than to KwaZulu-Natal.

Although our results from the multiple optimization analyses show fairly wide variation in the GRAS, our results show much lower variation in the outcome in terms of the benefit of the utilitarian plan in comparison with the egalitarian plan. Specifically, in terms of the percentage increase in HIV IP in women by the utilitarian plan in comparison with the egalitarian plan (Table 1). There is less variation in the benefit because the short-term efficiency of interventions is likely to be very similar in Mpumalanga and KwaZulu-Natal (Fig. 7C); consequently the GRAS for the utilitarian plan (over the identified range in Table 1) has relatively little effect on the additional number of HIV IP. If adherence is moderate the benefit of the utilitarian plan in comparison with the egalitarian plan is slightly less than when adherence is high (Table 1). Notably, the results from the initial optimization analysis for the benefits of the utilitarian plan in comparison with the egalitarian plan are within the Inter-Quartile Ranges obtained from the multiple optimization analyses (Table 1).

Results in Fig. 9 are from the multiple optimization analyses which include uncertainty in parameter estimation when calculating both the utilitarian and egalitarian strategy, see Methods. In both Fig. 9A and 9B the results for the utilitarian strategy are based on assuming that the optimal implementation plan is to divide resources between KwaZulu-Natal and Mpumalanga; the range for the GRAS that is used is shown in Table 1. Fig. 9A shows the number of HIV IP in women in each province in the first year of the rollout, assuming 50 million microbicides are available: grey data show the results of the egalitarian plan (solid grey columns based on high adherence, striped grey columns on moderate adherence) and red data show the results of the utilitarian plan (solid red columns based on high adherence, striped red columns on moderate adherence). The results in Fig. 9B are qualitatively similar to those shown in Fig. 9A; but they are quantitatively different as they are based on assuming 100 million microbicides are available. Clearly, HIV infections would be prevented in only two provinces if the utilitarian rollout plan is used, but in every province if the egalitarian plan were used. Not surprisingly, regardless of whether the rollout plan is based on the utilitarian or the egalitarian principle, the greater the resource constraints and/or the lower the adherence the fewer the number of HIV IP (Fig. 9A and 9B).

Efficacy is the degree of protection against infection conferred by a microbicide if adherence is 100%. Effectiveness is the degree of protection against infection conferred by a microbicide at a given level of adherence.

The HIV effectiveness results of the CAPRISA 004 trial were reported for three adherence levels ⁵. Low adherence is defined as using the microbicide in < 50% of sex acts. Moderate adherence is defined as using the microbicide in 50–80% of sex acts. High adherence is defined as using the microbicide in > 80% of sex acts. At low, moderate and high adherence levels the effectiveness of the microbicide in protecting against HIV infection was 28%, 38% and 54%, respectively ⁵. The effectiveness of the microbicide in protecting against HSV-2 infection was 51% and was not stratified by adherence ⁵.

We defined three adherence levels (low, moderate and high) as in the CAPRISA trial and specified the effectiveness of the microbicide in protecting against HIV infection at each level based on the trial results ⁵. Based on the trial results, we specified the effectiveness of the microbicide in protecting against HSV-2 infection to be 51% at all three adherence levels ⁵.

The geospatial meta-population transmission (MT) model includes the spatial demographics of South Africa, the within-country geographic variation in HIV prevalence and incidence, the province-specific rollout of treatment (with coverage increasing from 2004 onwards, Supplementary Fig. 1) and geographic heterogeneity in sexual behavior. The model consists of 33 non-linear ordinary differential equations. The equations specify the transmission dynamics of coupled HIV and HSV-2 epidemics; the equations are given in Section C.3 of the Supplementary Methods.

The model includes coupled HIV and HSV-2 epidemics because each virus affects the transmission of the other virus ^29–32. HIV infection increases the risk of transmitting HSV-2 ²⁹, conversely HSV-2 infection increases the risk of transmitting HIV ³³. In addition, HSV-2 infection increases the risk of acquiring HIV ^34,35. All of our analyses are based on the assumption the microbicide could potentially reduce both HIV and HSV-2 transmission; we made this assumption because the CAPRISA microbicide was found to be partially effective against both HIV and HSV-2 ⁵.

The model is gender-stratified and includes susceptible individuals, individuals infected with only HIV, individuals infected with only HSV-2, and individuals co-infected with both HIV and HSV-2. The natural history of HIV is modeled as a series of three stages, characterized by CD4 level and viral load (which determines infectivity); HIV-infected individuals on treatment are also tracked. The natural history of HSV-2 is modeled as two alternating states: the infectious state (when individuals shed virus) and the noninfectious state (when the virus is latent). Individuals co-infected with both viruses are modeled to reflect modifications in infectivity and susceptibility due to HIV or HSV-2 infection.

The model is based on the parsimonious assumptions that there is homogeneous mixing within a province, and negligible (at the population level) sexual mixing among individuals living in different provinces. See Section C in the Supplemental Methods for further details on model structure, a flow diagram is given in Supplementary Fig. 6. The model was simulated using MATLAB.

The geospatial MT model was parameterized using demographic, behavioral and treatment data from South Africa; ranges were specified for each parameter. Supplementary Table 4 provides a summary of all model parameter symbols and definitions. Parameter ranges are provided in Supplementary Tables 3, 5, 6 and 7. Province-specific parameters are provided in Supplementary Table 3. Supplementary Table 5 gives antiretroviral therapy and microbicide parameters. Supplementary Table 6 gives HIV parameters; Supplementary Table 7 gives HSV-2 parameters. Each parameter was sampled 1,500 times using Latin Hypercube Sampling (LHS) ^36–38.

The parameter set, obtained using LHS ^36–38, was used for calibrating the geospatial MT model. Calibration was based on an iterative multi-stage procedure that includes Monte Carlo filtering; see Section C.5 in the Supplementary Methods. The model was calibrated for both women and men in each of the nine provinces for the year 2004, when HIV prevalence in South Africa appears to have stabilized (Supplementary Fig. 7) and treatment was introduced. It was calibrated by fitting to gender-stratified province-specific estimates of HIV prevalence for 2004 generated by the most recent version of the Actuarial Society for South Africa (ASSA) AIDS and Demographic model ³⁹. The calibration resulted in 1,362 estimates for gender-stratified HIV incidence rates and prevalence levels for each of the nine provinces for the year 2004. After the model was calibrated, it was verified (see Section C.6 in the Supplementary Methods) and validated (see Section C.7 in the Supplementary Methods).

We used response hypersurface modeling and LHS ^36–38 to conduct multivariate sensitivity analyses of the geospatial MT model ^{36, 40}. We determined the effect of microbicide coverage and effectiveness on reducing HIV and HSV-2 transmission in both genders over a decade in KwaZulu-Natal province. Coverage is defined as the percentage of women who are uninfected with HIV (regardless of whether they are infected with HSV-2) and who use the microbicide. We used the 1,362 simulations that had been calibrated to 2004; we introduced province-specific treatment rollout (Supplementary Fig. 1), ran the simulations to the current year and then introduced microbicide-based interventions. The parameter values used are specific to KwaZulu-Natal; see Supplementary Table 3. The rollout of microbicides was modeled for 10 years; see Section C.2 in Supplementary Methods and Supplementary Fig. 8. Throughout this time we also modeled the planned continued expansion of treatment; see Section C.1 in the Supplementary Methods and Supplementary Fig. 1. We varied microbicide coverage rates from 30–90%, HIV effectiveness from 15–75% and HSV-2 effectiveness from 30–75%. The reduction in HIV and HSV-2 transmission due to microbicides, over a decade, was calculated. Response hypersurfaces were then fitted to these results.

We conducted scenario analyses of the geospatial MT model to examine the effect of microbicide coverage and effectiveness on reducing HIV and HSV-2 transmission in KwaZulu-Natal province where the CAPRISA 004 trial was conducted; parameter values are given in Supplementary Table 3. The six scenarios are based on different assumptions regarding coverage (60% or 90%) and adherence (low, moderate or high). Low, moderate and high adherence corresponds to an effectiveness of the microbicide in protecting against HIV infection of 28%, 38% and 54%, respectively. In all six scenarios the effectiveness of the microbicide in protecting against HSV-2 infection is 51%. The remaining parameter values used to generate the scenarios are the median values of the distributions shown in Supplementary Tables 3, 5, 6 and 7.

We conducted four uncertainty analyses of the geospatial MT model. These analyses were based on: (i) high coverage (90%) and high adherence, (ii) high coverage (90%) and moderate adherence, (iii) moderate coverage (60%) and high adherence, and (iv) moderate coverage (60%) and moderate adherence. The adherence-effectiveness relationship we modeled was determined from the results of the CAPRISA trial ⁵. To model high adherence, we used a triangular distribution for effectiveness against HIV ranging from 34%–74% with a peak density at 54% ⁵. To model moderate adherence, we used a triangular distribution for effectiveness against HIV ranging from 18%–58% with a peak density at 38% ⁵. For all four uncertainty analyses, we used a triangular distribution for effectiveness against HSV-2 ranging from 31%–71% with a peak density at 51% ⁵.

For each uncertainty analysis, and for each of the nine provinces, we used the 1,362 simulations that had been obtained from the calibration procedure. The model had been calibrated to 2004 when the rollout of treatment began in South Africa. Therefore, we introduced treatment into each of the simulations beginning in 2004. We used different treatment rollout rates in each province; see Section C.1 of the Supplementary Methods and Supplementary Fig. 1. We continued modeling the roll out of treatment in each province to the current year at which point we introduced interventions. Therefore we had 1,362 estimates for the gender-stratified pre-intervention HIV incidence rates and prevalence levels in each province. The GRAS for the egalitarian rollout plan was used to divide the available supply of microbicides among the nine provinces. The proportion of the supply that each province was allocated equaled the number of HIV-negative women who live in the province divided by the total number of HIV-negative women who live in SA. The modeling of the rollout of microbicides is described in Section C.2 of the Supplementary Methods, and shown in Supplementary Fig. 8. When conducting the uncertainty analyses, as well as the historical rollout of treatment beginning in 2004, we included the planned province-specific expansion of treatment; see Section C.1 of the Supplementary Methods and Supplementary Fig. 1

We used the uncertainty analyses to predict the cumulative number of HIV IP (over a decade) by interventions in each province. When we made predictions we excluded the effect of expanding treatment coverage on reducing transmission. This was accomplished by running each scenario in each uncertainty analysis twice: once with interventions and expanding treatment coverage, and once with only expanding treatment coverage. The difference between the two scenarios is the number of HIV IP by microbicide-based interventions. Results from these analyses were then mapped.

Predictions generated by the uncertainty analyses were used to calculate the long-term (i.e., over a decade) efficiency of interventions in reducing HIV transmission in both genders in each province; the results were then mapped. Long-term efficiency was defined as the number of women-years on microbicide needed to prevent one HIV infection in either gender. Women-years were calculated by multiplying the number of women using microbicides each year with the number of years of microbicide usage.

Predictions generated by the uncertainty analyses were plotted and used to identify a statistical relationship between the pre-intervention HIV incidence rate in women and the long-term efficiency of interventions in reducing HIV transmission in both genders. We also conducted regression analyses to determine the value of y: where y represents the median number of women-years necessary to prevent one HIV infection in women. We determined the value of y assuming either high or moderate adherence. Based on data from the CAPRISA trial⁵ we assume high adherence corresponds to using microbicides in 85% of sex acts and moderate adherence to using microbicides in 65% of sex acts.

The predictions generated by the uncertainty analyses were used to calculate the short-term efficiency of interventions (i.e., the efficiency in the first year of the rollout) in each province. Short-term efficiency was defined as the number of HIV IP per 10,000 microbicides used. This equals 10,000/2ycau where y represents the median number of women-years necessary to prevent one HIV infection in women and 2cau is the total number of microbicides used (on average) per year by each woman. In the expression 2cau, c is the average number of new sex partners per woman per year, a the number of sex acts per partnership and u the proportion of sex acts for which microbicides are used according to the CAPRISA 004 protocol (i.e., u represents adherence). Since the protocol was based on using a microbicide before and after sex ⁵, the factor 2 is included in the equation. We calculated the short-term efficiency of interventions in each province by using province-specific values for y and c. We calculated province-specific estimates of y by dividing the number of HIV IP by the number of women-years on microbicide for each of the 1,362 simulations. Province-specific values for c were estimated during the calibration of the geospatial MT model; the range is given in Supplementary Table 3. The range of estimates for a is given in Supplementary Table 6. We calculated short-term efficiency of interventions assuming either high or moderate adherence. Based on data from the CAPRISA trial ⁵, we assume high adherence corresponds to using microbicides in 85% of sex acts and moderate adherence to using microbicides in 65% of sex acts.

The geospatial resource allocation (RA) model was based on the parsimonious assumption that, over one year, HIV prevalence does not change substantially and the number of HIV IP in men (due to women using microbicides) would be negligible. The model operates under two constraints: the total number of microbicides that are available in the first year of the rollout (i.e., the amount of resources) and adherence.

The geospatial RA model was parameterized using province-specific estimates for the number of 15–49 year old HIV-negative women residing in the province, the average number of new sex partners per woman per year, and the pre-intervention HIV incidence rate in women. The number of 15–49 year old HIV-negative women in each province was calculated by multiplying the total number of 15–49 year old women in the province with the proportion of women in that province that are not infected (i.e, one minus the pre-intervention HIV prevalence level). The total number of 15–49 year old women in each province was based on estimates from the most recent version of the ASSA AIDS and Demographic model ³⁹. Ranges for province-specific estimates for the average number of new sex partners per woman per year were obtained from the calibration of the geospatial MT model. Pre-intervention HIV incidence rates and prevalence levels were obtained from the uncertainty analyses of the geospatial MT model.

Under the egalitarian rollout plan the supply of resources (i.e., microbicides) is divided among the nine provinces in proportion to the number of women in need of protecting against HIV infection. Specifically, the percentage of the supply that a province is allocated is equal to the number of 15–49 year old HIV-negative women who live in that province divided by the total number of HIV-negative women (in the same age group) who live in SA. For each province, we calculated the number of HIV-negative women in the province by multiplying the number of 15–49 year old women in the province ³⁹ with the proportion of women in that province that are not infected (i.e, one minus the pre-intervention HIV prevalence level). The total number of 15–49 year old women in each province was based on estimates generated by the most recent version of the ASSA AIDS and Demographic model ³⁹. We calculated a GRAS for the egalitarian plan that included uncertainty in estimating the pre-intervention HIV prevalence levels in women, and another without uncertainty. To include uncertainty we used province-specific ranges for the pre-intervention HIV prevalence levels obtained from the uncertainty analyses of the geospatial MT model. To calculate the GRAS for the egalitarian plan without uncertainty we used the median value of the range for each province.

The number of HIV infections prevented in each of the nine provinces (under the egalitarian plan) is calculated as the product of the number of HIV-negative women (aged 15–49 years old) who reside in that province, the pre-intervention incidence rate in that province, the proportion of HIV-negative women (in that province) who use microbicides, and the effectiveness of the microbicide. Summing over all provinces gives the total number of HIV IP.

Throughout our description of the optimization analyses when we refer to women we are referring to women who are 15–49 years old. We used the geospatial RA model and mathematical optimization techniques based on linear programming to calculate (under resource constraints) the GRAS that is necessary to implement the utilitarian rollout plan, the optimal geographic location to initiate a rollout based on the utilitarian principle, and the number of HIV IP in women in the first year of the rollout. We used the total number of HIV IP in women in South Africa as the objective function for the optimization analysis, and specified the resource constraint in terms of the total number of microbicides available in the first year of the rollout. The optimal solution is the GRAS that maximizes the total number of HIV IP in South Africa in the first year of the rollout; i.e., it is the GRAS for the utilitarian rollout plan. As the geospatial RA model considers only the first year of the rollout, the province(s) that are allocated resources in the optimal solution are the optimal geographic location(s) to initiate the rollout.

The optimization algorithm allocates the available resources disproportionally to the provinces where interventions are the most efficient; i.e., to the provinces that prevent the highest number of HIV infections for a given amount of resources. The efficiency of interventions in a province is equal to the number of HIV IP in that province in the first year of the rollout divided by the total number of microbicides used in that province. The number of HIV IP in each province, given a specific proportion of the supply of microbicides, is calculated as the product of the number of HIV-negative women who reside in the province, the HIV incidence rate in the absence of microbicides, the proportion of HIV-negative women who use microbicides, and the level of adherence (which specifies the degree of effectiveness of the microbicide in protecting against HIV). The total number of microbicides used in each province is calculated as the product of the number of HIV-negative women who reside in that province, the proportion of these women who use microbicides, the average number of new sex partners per woman per year, and twice the average number of sex acts per partnership. We assume women will use microbicides according to the CAPRISA004 protocol (i.e. once before and after sex ⁵). The optimization algorithm identifies the GRAS that would maximize the number of HIV IP in SA in the first year of a rollout. The optimization problem can be stated as the following linear program: Maximize∑i=19Ni(1-Pi)Iipxisubjectto∑i=192Ni(1-Pi)xiciau≤Yand0≤xi≤1 where

For each of the nine provinces, we used the parameter set (out of the 1,362 parameter sets obtained from calibrating the model) that generated the median value for the incidence rate. With these nine parameter sets, we used the geospatial MT model to calculate - for each province - the number of 15–49 year old women living in that province at the beginning of the rollout, the pre-intervention HIV prevalence level in women, the pre-intervention HIV incidence rate in women and the average annual number of new sex partners (N_i,P_i,I_i and c_i for i = 1..9, respectively). The x term is the result of the optimization, it specifies the proportion of eligible women in each province that receive microbicides in the first year of the rollout in order to maximize the total number of HIV IP in SA in the first year of the rollout. Hence it specifies the GRAS for the utilitarian rollout plan.

We calculated the GRAS under two levels of resource constraints, assuming either 50 or 100 million microbicides were available. Fifty million is enough for ~33%, and 100 million for ~66%, of the 15–49 year old HIV-negative women in SA. For each level of resource constraint we conducted two analyses, assuming either high or moderate adherence. Based on data from the CAPRISA trial ⁵, we assume high adherence corresponds to using microbicides in 85% of sex acts (resulting in an effectiveness against HIV infection of 54%) and moderate adherence to using microbicides in 65% of sex acts (resulting in an effectiveness against HIV infection of 38%).

We also conducted multiple (1,362) optimization analyses that included uncertainty in estimating the values of the province-specific pre-intervention HIV incidence rates in women, the pre-intervention HIV prevalence levels in women, and the average number of new sex partners per woman per year. We also included uncertainty in the number of sex acts per partnership. We included uncertainty by using parameter ranges. We used province-specific ranges for the pre-intervention HIV incidence rates and prevalence levels obtained from the uncertainty analyses of the geospatial MT model. Province-specific ranges for the average number of new sex partners per woman per year are given in Supplementary Table 3. The range for the average number of sex acts per partnership is given in Supplementary Table 6. In each of the optimization analyses the rank ordering of the provinces, in terms of incidence rates in women, was varied probabilistically.