Individual and Population Level Effects of Partner Notification for Chlamydia trachomatis

Partner notification (PN or contact tracing) is an important aspect of treating bacterial sexually transmitted infections (STIs), such as Chlamydia trachomatis. It facilitates the identification of new infected cases that can be treated through individual case management. PN also acts indirectly by limiting onward transmission in the general population. However, the impact of PN, both at the level of individuals and the population, remains unclear. Since it is difficult to study the effects of PN empirically, mathematical and computational models are useful tools for investigating its potential as a public health intervention. To this end, we developed an individual-based modeling framework called Rstisim. It allows the implementation of different models of STI transmission with various levels of complexity and the reconstruction of the complete dynamic sexual partnership network over any time period. A key feature of this framework is that we can trace an individual’s partnership history in detail and investigate the outcome of different PN strategies for C. trachomatis. For individual case management, the results suggest that notifying three or more partners from the preceding 18 months yields substantial numbers of new cases. In contrast, the successful treatment of current partners is most important for preventing re-infection of index cases and reducing further transmission of C. trachomatis at the population level. The findings of this study demonstrate the difference between individual and population level outcomes of public health interventions for STIs.

1 Heterogeneity in sexual behavior 1

.1 Risk class model
We develop a model with different sexual activity classes (risk class model) to take into account the heterogeneity in sexual behavior. The notation is based on the instantaneous contact model from the main text. Following Hethcote & Yorke [1] and Garnett et al. [2], we derive the following set of ordinary differential equations: Individuals are denoted by X i,k where the subscript i refers to the sex (1 − i being the opposite sex for i ∈ {0, 1}) and the subscript k refers to one of n sexual risk classes. The superscripts S and I indicate whether individuals are susceptible or infected. Susceptible individuals X S i,k seek sexual partners at rate c k and become infected with Chlamydia trachomatis by their infected partners X I 1−i,l with a per partnership transmission probability β kl . The average infectious duration is given by 1/γ. ρ i,kl denotes the sexual mixing matrix for an individual of sex i that belongs to risk class k and makes contact to individuals in risk class l. It can be defined as with X 1−i,l being the proportion of partners that belongs to sexual risk class l and where δ kl denotes the Kronecker delta (it is equal to 1 if k = l and to 0 otherwise). Mixing can be varied between proportionate (ε = 0) and fully assortative (ε = 1). The duration that individuals remain in this population (16-25 year old) is 1/µ, i.e., 10 years. The model is parameterized with sexual behavior data of 16-25 year old women and men from the UK National Survey of Sexual Attitudes and Lifestyles (Natsal) 2000 [3]. We assume two risk classes (n = 2, for low and high sexual activity) and use maximum likelihood estimation to obtain the proportion of individuals in each risk class X k and the risk-class specific sexual partner change rate c k [4]. Data for women and men are pooled, i.e., we assume the same sexual behavior for both sexes. Assuming that the realized number of heterosexual partners during one year for individuals of risk class k follows a Poisson distribution with mean c k , we estimate that 94.6% and 5.4% of individuals belong to the low and high risk class, respectively (Fig. S2A). The corresponding heterosexual partner change rates are 0.61 and 8.05 per year.
We assume that the per partnership transmission probability for contacts between individuals of the low risk class and individuals of the high risk class, β 12 = β 21 , is 50%. This is in the range that has been estimated in a medium risk setting [5]. The per partnership transmission probabilities for contacts between two individuals of the low risk class or two individuals of the high risk class are obtained by a scaling factor α, i.e., we define β 11 = αβ 12 and β 22 = β 12 /α. For α = 1.9 and an average infectious duration of 1 year [6,7], we obtain an endemic C. trachomatis prevalence of 3% (β 11 = 95% and β 22 = 26.3%). The structure and parameters of the deterministic, population-based model are then implemented in Rstisim in an individual-based manner. Assuming proportionate mixing (ε = 0), we obtain a more clustered sexual contact network (Fig. S2B) compared to a homogeneous population (see main text) and a realistic distribution of C. trachomatis infections in the population (Fig. S3). Note that increasing ε towards assortative mixing results in most C. trachomatis infections being concentrated among high risk individuals which is not consistent with population-based data from Natsal 2000 [8].

Individual level effect of partner notification
The C. trachomatis-positivity of partners of infected index cases in the risk class model together with the results from the instantaneous contact model and the pair model from the main text is shown in Fig. S4. The C. trachomatis-positivity in the most recent partner is lower in the risk class model than the models that assume homogeneous mixing (Fig. S4A) because the transmission probability per partnership in the risk class model is lower. Only contacts between individuals of the low risk class result in a high transmission probability (β 11 = 95%), which is necessary to obtain the high C. trachomatis-positivity of partners as found in the study by Carré et al. [9].The third and subsequent partners are also more likely to be chlamydia positive than the overall population. This is because the infections tend to be concentrated among high risk individuals (Fig. S3), who have higher partner change rates and a higher prevalence of C. trachomatis than the overall population. When partners  are grouped by the time period since the partnership has ended, C. trachomatis-positivity is > 10% as far back as 18 months. The proportion of infected partners in the risk class model is lower than in the instantaneous contact model but similar to the pair and triple models (Fig. S4B).

Population level effect of partner notification
The effects of screening and PN in the risk class model are shown together with the results from the instantaneous contact model and the pair model from the main text (Fig. S5). As for the pair model, most of the additional reduction in prevalence stems from notifying the most recent partner (Fig. S5A). The effects of different PN periods in the risk class model are very similar to those in the instantaneous contact model that assumes homogeneous mixing. Increasing the PN period results in a slight but steady decrease in prevalence (Fig. S5B). This is because the contact with the most recent partner has usually happened sometime during the past year because neither model explicitly accounts for ongoing (current) sexual partnerships. In summary, our conclusion from the main text, that notifying the most recent partner generates most of the additional effect that PN has on reducing C. trachomatis transmission, is robust to the assumption of heterogeneity in sexual activity.

Sex-specific differences in duration of infection
This scenario uses the pair model from the main text. We assume that the infectious duration in men (6 months) is half of that in women (12 months) and adjust the transmission probability so that the endemic prevalence of C. trachomatis is 3%. A per sex act transmission probability of 25.1% results in a prevalence of 3.1% and 2.9% in women and men, respectively. Our conclusions, both for the C. trachomatis-positivity in partners (Fig. S6A)  the same as those drawn from the pair model in the main text.

Differences in uptake of screening and partner notification
These scenarios use the pair model from the main text. The prevalence of C. trachomatis can be substantially reduced (Fig. S8) at higher screening rates or higher probabilities of successful PN than in the baseline scenario. We also studied the scenario when only women are screened (S9) and find the same behavior. For example, the C. trachomatis prevalence can be reduced to about 30% of the pre-screening levels if all women are tested every other year (which corresponds to a screening rate of 0.5 per year) and if 50% of the current partners are notified and successfully treated (S9D).  Figure S9: Reduction of C. trachomatis prevalence for different screening (only women) and partner notification scenarios in the pair model. Left panels: Prevalence of C. trachomatis for different numbers of notified partners. Right panels: Prevalence of C. trachomatis for different partner notification periods. The probability that a notified partner is tested and successfully treated is 10% (A and B), 50% (C and D) and 90% (E and F).
Only women are screened with rates as indicated. All other parameters are as given in the main text.