Effectiveness of a no-sex or safe-sex month in reducing HIV transmission
Benjamin Armbruster a & Aaron M Lucas a
a. Department of Industrial Engineering and Management Sciences, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, United States of America.
Correspondence to Benjamin Armbruster (e-mail: firstname.lastname@example.org).
(Submitted: 29 March 2011 – Revised version received: 25 January 2012 – Accepted: 02 February 2012 – Published online: 11 April 2012.)
Bulletin of the World Health Organization 2012;90:504-512. doi: 10.2471/BLT.11.088641
Despite significant investment in programmes for the treatment and prevention of human immunodeficiency virus (HIV) infection, the prevalence of such infection in sub-Saharan Africa remains stubbornly high. In 2009, for example, an estimated 24.8% of the adults living in Botswana and 17.8% of those living in South Africa were thought to be HIV-positive.1 Prevention is, in general, particularly poor: for every two individuals starting treatment, five become infected with HIV.2 Recently, many international organizations, including the Joint United Nations Programme on HIV/AIDS (UNAIDS), The World Bank and the World Health Organization (WHO), have called for a realignment of prevention strategies and new, innovative ways to blunt the impact of the HIV epidemic, especially in those countries that are most affected.3,4 A novel strategy proposed by Parkhurst and Whiteside5 – a population-wide “month off” from risky behaviour, with no sex or exclusively safe sex over that period – gained a substantial amount of publicity, with articles6–8 and mentions9–14 in many high-profile outlets. Unlike most other interventions seeking to modify sexual behaviour, this strategy expects participants to change their behaviour for a relatively short time, albeit once a year. It may also have relatively low set-up and promotional costs. Furthermore, such a “month-off” intervention has the potential for creating a strong national movement5 and at least two countries, Kenya and Swaziland, are already considering campaigns based on this intervention.6,15
As Parkhurst and Whiteside state in their discussion, the crux of the intervention they propose lies in forcing many individuals who are newly infected with HIV to pass through the acute stage of their infection without engaging in any behaviour that may be risky in terms of the transmission of the HIV.5 The acute phase of HIV infection, which lasts roughly 2 months, is associated with high rates of infectivity.5 Infectivity drops dramatically following the acute stage and then remains low for several years, until the development of acquired immunodeficiency syndrome (AIDS).16 A month-long break in risky behaviour could substantially reduce the viral load in a population, not only by interrupting all transmission for a month but also by cutting the number of individuals who are in the acute stage of HIV infection when the risky behaviour resumes. It has been suggested that the prevalences of HIV infection in countries with large Muslim populations are kept relatively low by the Muslim practice of abstaining from sex during the daylight hours of the month of Ramadan.5
Since a clinical trial of an annual, month-long break from risky behaviour would be unethical and pose huge logistical problems, Parkhurst and Whiteside suggested that such an intervention should be mathematically modelled, to guide future policy discussions.5 We therefore constructed a model to assess the impact of a month-long interruption in HIV transmission (the “test intervention”) on the prevalence and incidence of HIV infection in three countries in sub-Saharan Africa: Kenya, South Africa and Swaziland. While South Africa was modelled simply as an example of a country where HIV infection is hyperendemic, Kenya and Swaziland were investigated because their governments are considering implementing the test intervention. The model was used to evaluate the potential benefits of the test intervention and to give insight into the associated policy debate.6,15
Our model replicates the characteristics of the HIV epidemics in Kenya, South Africa and Swaziland. Each of these countries represents a hyperendemic setting for which the relevant data on HIV prevalence and demographics are readily available. The model focuses on the progression of HIV-1 infection among adults aged 15–49 years. The relevant demographic information was provided by the United Nations Population Division.17
We constructed a simple deterministic model of transmission, illustrated in Fig. 1, that divides the population into several compartments. Table 1 lists the parameters for the model. The model tracks the number of individuals in each compartment over time by using state variables (S, I1, I2, I3, I4, I5, I6 and I7), and it describes the flow of individuals among the compartments by using the differential equations outlined in Appendix A (available at: http://users.iems.northwestern.edu/~armbruster/Armbruster2012-BullWHO-AppendixA.pdf). The system of differential equations was simulated in version 7.9.0 of the MATLAB software package (MathWorks, Natick, United States of America) using the ODE solver, ode45. Each modelled population was divided into eight compartments: one compartment, S, for uninfected, susceptible individuals; five compartments, I1 to I5, for individuals in different stages of HIV infection who are not receiving antiretroviral therapy (ART); and two compartments for individuals on ART, I6 and I7. The rates σ1 to σ7 define the annual transition rates between compartments. Compartment I1 contains individuals in the acute stage of HIV infection; I2, I3 and I4 contain those in the chronic stage, and I5 contains those in the final stage, who have AIDS. We chose to split the chronic stage into three compartments so that the survival time without ART gave a good fit to a Weibull distribution with a median survival of 11 years. This distribution fits the data collected during the CASCADE collaboration study well.16,27
Fig. 1. The compartmental model used to explore the effectiveness of two interventions for the control of human immunodeficiency virus (HIV)
Table 1. Parameters used in the models of HIV transmission in Kenya, South Africa and Swaziland, and their sources
The sum of the sizes of each of the eight compartments, S + ΣjIj, gives the size of the total modelled population, N. We defined α as the transmission rate in the chronic stage. The transmission rate aggregates several factors influencing HIV transmission, such as heterogeneity in sexual risk, coital frequency, rates of new partners and rates of condom use. While these factors, and the consequent transmission rate, may change over the course of the epidemic, it is reasonable to assume that they remain constant over the 1-year and 5-year horizons that we considered (May et al.28 gave an in-depth discussion of transmission rates in compartmental models). The multiplier, λj, denotes the infectivity of individuals in compartment Ij relative to that of individuals in the chronic stage of infection, such that, for example, the transmission rate in the acute stage is λjα. We used the same values for the relative infectivity rates, λj, and for the durations of the various stages of infection that Granich et al. used for their stochastic model.16 Granich et al. estimated the relative infectivities in the acute and final stages of HIV infection, λ1 and λ5, by comparing three analyses29–31 of the data collected in Rakai, Uganda, on HIV transmission in serodiscordant couples.32 Since Hollinsworth et al. estimated that the acute stage lasts 3 months and is 26 times as infectious as the chronic stage30, in the sensitivity analysis we considered scenarios in which σ1–1 was set to 3 months and λ1 was set to 26. We also considered scenarios in which those in the final stage of HIV infection without ART: (i) do not contribute to new infections, so that λ5 is zero; (ii) contribute to infections and are more infectious than assumed in the base case, with λ5 set to 7; or (iii) have a relatively short survival time, with σ5–1 set to 9 months.
Following Granich et al.,16 we assumed that, after the acute stage, an HIV-positive person’s count of CD4+ T-lymphocytes (CD4) drops to a mean of 774 cells/µl and then shows a subsequent linear decline, of about 72 cells per µl each year, until the person’s death. The rate in decline of CD4 counts after the acute stage is calculated on the assumption that the median time until death without ART is 11 years. Thus, using the durations shown in Table 1, the individuals in compartments I4 and I5 are estimated to have CD4 counts of 335 and 116 cells/µl, respectively. According to guidelines published by WHO in 2006 and 2010, individuals in compartment I5 (2006 guidelines) or individuals in compartments I4 and I5 (2010 guidelines) are eligible for ART.33,34 The proportions provided in the 2010 UNAIDS global report1 were used to calculate the annual per capita entry rates into the ART compartments by equating the inflow to each ART compartment with the outflow. To estimate the lifespans of HIV-positive individuals undergoing treatment, as affected by CD4 counts when treatment began, we used the results of a recent analysis of data from a large cohort study in Uganda.26 These results were stratified by initial CD4 count and also by 5-year age groups. The life expectancies of individuals aged 30–34 years who had 0–49, 50–99, 100–149, 150–249 and ≥ 250 CD4 cells/µl when they initiated ART were 14.2, 24.7, 36.0, 40.3 and 37.2 years, respectively. We took the mean for the first three CD4 groups in this age group, 25.0 years, as the life expectancy for those entering treatment from I5 and the mean for the last two CD4 groups, 38.75 years, as the life expectancy for those initiating treatment from I4.
The UNAIDS’ Estimation and Projection Package (EPP)18 was used to project the HIV prevalences in the three test-bed countries for 2011 and 2013. As suggested by the documentation that forms part of this software package, serosurveillance data from both population-wide surveys and antenatal clinics were used as inputs. Historical data from UNAIDS1,19 on treatment coverage were also included. For South Africa, the results of a nationwide survey in 2008 and the prevalence time-series from a 2009 survey of antenatal clinics were used.20,21 For Kenya and Swaziland, Demographic Health Survey (DHS) serosurveillance data and prevalence histories recorded by antenatal clinics were employed.22–25 Among adults living in South Africa in 2009, the HIV prevalence estimated using the EPP, 17.6%, was close to the estimates made by UNAIDS1 and Statistics South Africa,35 which were 17.8% and 17.0%, respectively. Similarly, the corresponding EPP estimates for Kenya and Swaziland in 2009, 25.7% and 5.9%, respectively, were close to the estimates made by UNAIDS, which were 25.9% and 6.3%, respectively.1
We set the initial number of infected individuals in compartments I1 to I7 so that overall prevalence, (ΣjIj)/N, matched the EPP projection for 2011 and, initially, the inflows to compartments I2 to I7 matched the outflows. It seemed reasonable to match the inflows with the outflows because the EPP projections of prevalence are quite flat around 2011 for all three countries that were modelled. In the year 2010, the South African National Department of Health, while discussing the HIV epidemic in South Africa, stated that “the national estimate and provincial figures indicate a stable prevalence over the past four years.”21 Despite this reported or presumed stability in prevalence, epidemics initiating with 50% more individuals in treatment or with twice as many individuals with acute infection than assumed in a steady-state scenario were modelled in the sensitivity analysis.
The annual transmission rate for the chronic stage, α, was set so that the model-estimated prevalences matched the EPP projections. For this, a calibrated annual rate was found by the least-squares minimization of the differences between the model-estimated prevalences for the years 2011 and 2013 and the corresponding prevalences estimated in the EPP. For some scenarios in the sensitivity analysis – those that affected the goodness of the fit between the model-derived estimates and the EPP projections – α was recalibrated so that, for the year 2013, the model-derived prevalence again matched the EPP projection.
Modelling the intervention
In the proposed intervention, the population of a country is mobilized to engage in total abstinence or safe sex for 1 month each year. In the present study, this “test” intervention was modelled by eliminating HIV transmission (i.e. setting the transmission rate α to 0) throughout the first month of every year. This assumes 100% compliance in the intervention and that the intervention does not lead to other changes in behaviour, such as increased risky behaviour during the other 11 months of each year. In the sensitivity analysis, we considered a scenario with 50% compliance, one with a 2-week period of no transmission, and one with a 2-month period of no transmission. We compared the modelled effects of the test intervention with the status quo and also with a hypothetical “alternative” intervention that reduces HIV transmission by one twelfth. (For the above three scenarios in the sensitivity analysis, the transmission factors for the alternative intervention are reduced by factors of 0.5/12, 14/365 and 2/12, respectively.) It was assumed that a comparison of the effects of the test and alternative interventions would highlight the “interruption effect” of the test intervention, that is, the effect of concentrating transmission control into a single month each year rather than spreading it throughout the year. We simulated the status quo, the test intervention and the alternative intervention over 1 year (until 2012) and over 5 years (until 2016) and compared the modelled HIV infection prevalences and numbers of new infections. No attempt was made to simulate the effects of the test intervention over longer timescales because any such intervention would need to prove itself quickly and because those who initially suggested the potential benefits of a yearly month without HIV transmission stated that this intervention was meant to be short-term.5–7 To focus on the two modelled interventions, we assumed that no additional interventions were initiated during the study period and that, under the status quo, the epidemic followed the calibrated model.
Table 2 and Fig. 2 show the results for the base case scenarios. Compared with the status quo, the test and alternative interventions each resulted in slightly fewer new infections and a slightly lower prevalence at the end of the modelled period. In all three countries that were modelled, over both 1-year and 5-year periods, the decrease in prevalence seen with the test intervention, if any, was nearly identical to that seen with the alternative. In Kenya, for example, over a 1-year period, the number of new infections was about 0.5% of the initial population, whether the status quo, the test intervention or the alternative intervention was modelled. Over a 5-year period, the alternative intervention allowed more new infections, as a percentage of the initial population, than the test intervention but the difference was slight (0.01%). In South Africa, over a 1-year period, both the test intervention and the alternative reduced the number of new infections, from roughly 1.2% of the initial population under the status quo to about 1.1% under either intervention. Similarly, over a 1-year period in Swaziland, both the test intervention and the alternative reduced the number of new infections, from about 1.9% of the initial population under the status quo to about 1.8% under either intervention. Note that, wherever the effectiveness of the test intervention and the alternative are shown as identical in the main text, this apparent identity is the result of rounding and hides minor differences that may have affected calculations.
Table 2. Main results from the models of the base case scenarios for human immunodeficiency virus (HIV) transmission in Kenya, South Africa and Swaziland
Fig. 2. Modelled prevalences of human immunodeficiency virus (HIV) infection from 2011 to 2016, as seen under the status quo, the test intervention and the alternative intervention
For South Africa, the test intervention and the alternative averted, respectively, about 9.3% and 9.0% of the new infections seen under the status quo, when applied for 1 year. The corresponding results for Kenya and Swaziland were similar (Table 2). In all three countries that were modelled, the number of new infections averted over a 1-year period with the test intervention or the alternative was slightly more than one twelfth (8.3%) of the new infections seen when neither intervention was applied. Over a 1-year period, the test intervention averted roughly 2.5%, 3.3% and 1.6% more new infections than the alternative in Kenya, South Africa and Swaziland, respectively.
In South Africa, over 5 years, the number of new infections was about 5.9% of the initial population under the status quo and about 5.3% under either the test intervention or the alternative. Each intervention therefore averted about 10% of the new infections under the status quo, although the test intervention averted approximately 2% more new infections than the alternative. In Kenya and Swaziland, similarly, the test intervention averted 2% and 1% more new infections than the alternative when run over 5 years, respectively. Unsurprisingly, the number of new infections seen over 5 years in each country was close to five times the number seen over 1 year. The percentage of the new infections seen under the status quo that were averted under either intervention was, however, slightly higher over 5 years than over 1 year because averting infections in the first year reduces the numbers of new infections that occur in subsequent years.
The results of the sensitivity analysis are summarized in Table 3. As expected, the number of averted infections was roughly halved when compliance in the intervention was cut from 100% to 50% or when the test intervention was only run for 2 weeks instead of a month, and it was roughly doubled when the test intervention was run for 2 months. In general, in every scenario considered in the sensitivity analysis, the performance of the test intervention was very similar to that of the correspondingly adjusted alternative intervention. The test intervention averted slightly more infections than the alternative intervention except when it was applied at mid-year or at the conclusion of the year; then the last transmission-free period occurred so close to the end of 2015, the end-point for the assessment of effectiveness, that it had little if any detectable impact. The test intervention appeared most superior to the alternative intervention in the scenario in which the initial number of individuals in the acute stage was doubled (scenario 11). In that scenario, at the end of the first year, the test intervention outperformed the alternative, in terms of new infections averted, by 8%, 8% and 7% in Kenya, South Africa and Swaziland, respectively. However, most of the between-intervention differences seen were less than half of these values, and they were also smaller over 5 years than over 1 year.
Table 3. Main results from the sensitivity analysis of the model of human immunodeficiency virus (HIV) transmission in Kenya, South Africa and Swaziland
The effects of the test intervention appeared very similar to those of the alternative intervention. Although both of these interventions aim to reduce annual transmission of HIV by one twelfth, the test intervention concentrates this reduction into one month of zero transmission while the alternative spreads the reduction evenly throughout the year. Unsurprisingly, both interventions averted slightly more than one twelfth of the new infections, since averting infections reduces the numbers of infective individuals from which subsequent transmission can occur. That the differences between the test and alternative interventions, in terms of averted infections, were generally slight suggests that there is little benefit in concentrating transmission reduction into a month free of non-safe sex, primarily to reduce transmission from individuals in the acute phase of infection. The unique interruption effect of the test intervention, a month-long 100% decrease in risky behaviour, only seems to have a small, second-order role in reducing incidence when applied to the population at large; the overall reduction in transmission plays a larger role.
In the base case scenario, the between-intervention difference in the proportion of new infections averted was marginally less over a 5-year horizon than over a 1-year horizon. One possible explanation is that the turnover in the population (births and deaths) mitigates the effects of any intervention such that, over a relatively long period, the difference between the test intervention and the alternative would be less.
We used a straightforward, deterministic, compartmental, disease-transmission model to analyse the effects of the test intervention in three hyperendemic countries. Simple models have a long and successful history in the epidemiology of infectious disease and they are generally the rule rather than the exception. Prominent examples are Granich et al. (Lancet 200816), Williams et al. (PLoS Medicine 200636), Kahn et al. (PLoS Medicine 200637), and the EPP model used by UNAIDS for its HIV infection prevalence projections.18,38 Such models are used to understand the behaviour of a population-wide intervention and the magnitude of its effects. (Network and microsimulation models are well suited to situations where the intervention is tailored to the individual or their position in the sexual-contact network or across specific demographic groups.) Except for the differentiation of the stage of infectiousness, one limitation of our model is that it takes little account of the heterogeneity in sexual risk and sexual mixing. This may limit the model’s ability to quantify any intervention-attributable drops in prevalence and new infections precisely. However, such precise evaluation was not our aim. We merely sought to analyse the magnitude of the test intervention in relation to a comparable risk reduction spread throughout the entire year. Additionally, the introduction of any kind of heterogeneity would only be useful if we were modelling the participation of only select subgroups in the intervention or if we were concerned about the long-term stability of the epidemic, which we were not. Moreover, since the epidemic curve is calibrated to match the EPP projections, any fluctuations introduced by stratifying the model or doing away with proportionate mixing would be small. Lastly, since, in general, the scenarios we considered in our extensive sensitivity analysis did not greatly affect the performance of either the test or alternative intervention (the exceptions being scenarios 1–3, which assumed 50% compliance or varied the length of the test intervention by a factor of 2), we doubt that a modest incorporation of heterogeneity would have substantially changed the apparent performances of the interventions. We mainly modelled 100% compliance. With reduced compliance, having only a portion of the population participating in the intervention, the difference in effectiveness between the test intervention and the alternative would probably be only smaller.
In all of the modelled scenarios, we assumed that an equal proportion of individuals participated in the two interventions. If substantially more of the population participated in the month-long intervention than the alternative, then the month-long intervention might be more effective. It remains unclear, however, whether it would be more cost-effective to increase participation in the alternative intervention than to increase compliance in the transmission-free month.
Another limitation of the study is that no risk-compensation effects, such as individuals compensating, with additional risky behaviour, for the no-sex or safe-sex month, were considered in the model. The incorporation of such effects would decrease the effectiveness of both interventions. We were also conservative in assuming 100% compliance in the base case scenario. In fact, there is a possibility that the test intervention would increase risky behaviour by encouraging the non-compliers to seek out one another, allowing HIV to spread beyond existing partnerships.
We do not conclude that an intervention based on a yearly no-sex or safe-sex month would be ineffective, merely that it would be as effective as an alternative policy that spreads out the reduction in transmission across the whole year. Kenya and Swaziland are purportedly considering the promotion of a yearly month without non-safe sex.6,15 Since the effectiveness of such an intervention is not largely attributable to the unique “interruption” feature, the practicalities and costs of such an intervention, and compliance in it, should be compared with those of other ways of reducing aggregate HIV transmission, such as male circumcision, concurrency-reduction messages and condom-promotion strategies.
We thank Sabina Alistar, Elizabeth Barden, Stéphane Helleringer, David Hutton and Elisa Long for many helpful comments.
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