The concurrency index is a random number between 0 and 1 and is used to assign simulated humans into groups with different behaviors regarding the formation of concurrent partnerships. We define sexual activity groups in the model by associating with each group the desired annual contact rate cs (desired rate of forming a sexual partnership) and determining the proportion of men and women assigned to each of these groups. In this study, we aim to maintain the generally desired rate of contact in sexual activity groups (and thus the overall incidence of partnership) while allowing
In the case where ω=0.5, the rate of formation is simply the arithmetic mean of the desired female and male rates. An event in the Mukwano model is any event that can change the state of the network, e.g. Events occur sequentially in the model and are scheduled to occur using a calendar queue with a priority queue for each bucket [4].
Some events that occur in the model can force other events to occur before their scheduled time. We describe how births are planned in the model; from this the planning of other events can be derived. In particular, we set up our model so that the concurrency parameters θgk change at a given time in the model to reflect an intervention to reduce concurrency.
The way the model is set up, a reduction in the value of θgk will not affect the incidence of partnership as the overall contact rate Ngscgs for sexual activity groups.
Baseline scenario creation
Summary of plausible ranges for model inputs and outputs
Longer description of plausible ranges for model inputs
Three different sets of risk behaviors with different contact rates and concurrency parameters were modeled over time. The first lasted between the start of the model and year X, the second between year X and year Y, and the third between year Y and the end of the model. Men and women in the low-activity group were not allowed to form concurrent partnerships (i.e., θm=θf=0 for men and women in the low-activity group).
The contact rate for high- and low-activity males had an arbitrary value provided that the contact rate for high-activity males was higher than the contact rate for low-activity males. Women's contact rates were the same as men's contact rates in the same activity group and risk behavior set. The ratio of high-activity contact rate to low-activity contact rate remained constant across all risk sets.
Untreated HIV infection was roughly divided into four successive phases: primary HIV infection (Pri), post-primary CD4+ count more than 200 cells/μl (CD4>200), pre-AIDS CD4+ count less than 200 cells/μl (CD4<200PreAIDS), and an AIDS (AIDS) phase. ART was implemented by simulating the deletion of the CD4<200PreAIDS to the ARTFromPreAIDS phase and the deletion of the AIDS phase to the ARTFromAIDS phase. Stage duration was derived from a Weibull distribution with a mean of 0.25 years for primary stage, 7.9 years for CD4>200 stage, 2.1 years for CD4<200PreAIDS stage, 0.75 years for the AIDS and AIDSFromART stages, 6.4 years for the ARTFromPreAIDS stage and 2.25 years for the ARTFromPreAIDS stage.
Transmission probabilities were assumed to follow a bathtub distribution based on analysis by Hollingsworth et al [7] and data from Wawer et al. 391. ART was hypothesized to reduce transmission probabilities in the ARTFromPreAIDS and ARTFromAIDS stage and increase survival by a multiple of 3 [11].
Baseline fitting strategy
Supplemental Results
Empirical prevalence of concurrency and partnership distribution, and reported condom use
1.8% of men aged 15-24 reported having more than one relationship at the time of the interview. Using the same measure of coexistence, 23% of men aged 15–24 years reported coexistence in KwaZulu-Natal, South Africa in 2002 [ 12 ]. 8.5% of men aged 15-34 in the cohort who had ever had sex reported that they were still having sex with more than one of their last three sexual partners, compared to 21% in Botswana in 2007 [13].
15.9% of men with more than one partnership at the time of interview reported using a condom the last time they had sex, compared to men with only one partnership (p=0.04).
Baseline simulated scenarios
Simulated interventions
In the 20% reduction in competition intervention scenarios, the prevalence of long-term partnership contemporaneity in 2020 was between 25.3% and 33.9% lower in men and between 18.7% and 18.9% lower in women (where significant ) compared to baseline scenarios. Error: Reference source not found), and the prevalence of cohabitation of short duration partnership was between 20.2% and 23.6% lower in men and between 20.9% and 24.0% lower in women. In the 50% reduction in competition intervention scenarios, the prevalence of long-term partnership contemporaneity in 2020 was between 56.1% and 67.4% lower in men and between 45.9% and 47.7% lower in women (where relevant ) compared to baseline scenarios. and the prevalence of contemporaneous partnership of short duration was between 47.8% and 50.0% lower among men and between 52.1% and 55.9% lower among women. There was a sharp decline in the prevalence of total concurrence between 2010 and 2011 after the start of the intervention (Error: Reference source not found).
This was due to all the 'excess' short-term concurrent partnerships starting before the end of the intervention between 2010 and 2011. This was followed by a gradual decline in the prevalence of concurrent partnerships, as the 'excess' long-term concurrent partnerships started before the intervention ended. The full effect of the intervention on concurrency was reached by 2020, 10 years after the intervention, when all partnerships had started before the intervention ended.
There was very little difference in the incidence of partnering (Error: Reference source not found) or the average number of sexual acts per man per year (Error: Reference source not found) between the baseline and the corresponding intervention scenarios. The average annual incidence of partnership between 2011 and 2020 was between 0.04% lower and 0.08% higher in the intervention versions compared to the baseline versions. HIV incidence rates in 2020 with and without the tailored interventions and percentage reductions in incidence caused by the interventions are given in Figure 9.
The trend in HIV over time in the baseline and intervention scenarios (50% reduction in concurrency) for the best estimate scenario is shown in Error: Reference source not found. The declines in HIV incidence caused by differential declines in male and female co-occurrence are shown in .
Prevalence of concurrency and number of partners in 15-54-year-olds in the Masaka cohort in 2008. Either the proportion in the high-activity group or the proportion in the low-activity group was set equal to one to minimize the modeled value of theta. The ratio between high activity rate and low activity rate is the same in all risk behavior sets.
Adjusted reduction of concurrency parameters in the high concurrency group in the intervention scenarios after intervention initiation. The reported concurrency scenario simulated the reported prevalence of male and female cohabitation (ie 9.6% and 0%) 581. Long duration Short duration Total ratio of prevalence of men with a long-term partnership to the prevalence of men with a short-term partnership partnership with duration.
Ratio of prevalence of long-term partnership concurrence to prevalence of short-duration partnership concurrence. The credible ranges and model outputs for the prevalence of cohabitation and number of partners 592. Calculated as the difference in prevalence in the intervention scenario compared to the baseline scenario over the prevalence in the baseline scenario.
The distribution of partnerships in 2020 in baseline and intervention scenarios (20% and 50% reduction in concurrency). The change in HIV incidence over time in the best-estimated scenario after a 50% reduction in concurrency starting in 2010. Reported 'coincidence scenario: a) The target and the simulated male partnership distribution, b) the simulated female partnership distribution, and c. ) the model was fit to the empirical HIV prevalence in and 2007 and the trend in HIV prevalence.
The effect of the intervention (50% reduction in concurrency) on the prevalence of concurrency over time in the best-estimated scenario.
