Modelling the multiple anatomical site transmission of Mycoplasma genitalium among men who have sex with men in Australia

Mycoplasma genitalium (M. genitalium) is a recently recognised and important sexually transmitted infection among men who have sex with men (MSM). The role of oral sex, rimming, and kissing on M. genitalium transmission in MSM is unclear. We created four deterministic susceptible-infectious-susceptible epidemic models to examine the role that different sexual behaviours play in transmitting M. genitalium at the oropharynx, urethra anorectum among men who have sex with men in Australia. Our results suggest that oral and anal sex without other sexual practices (model 1) replicate well single site infection at the oropharynx, urethra and anorectum and also multi-site infection. If kissing or rimming are added to model 1 (i.e., model 2–4) no substantial improvements in the calibration of the models occur. Model 1 estimates that 3.4% of infections occur at the oropharynx, 34.8% at the urethra and 61.8% at the anorectum. Model 1 also estimates that the proportion of incident M. genitalium transmitted by anal sex was 82.4%, and by oral sex was about 17.6%. Our findings could provide an enhanced understanding of M. genitalium transmission in MSM, thus providing insights into what sexual practices contribute most to transmission.

www.nature.com/scientificreports/ that always using condoms for penile-anal sex in the last three months was a protective factor for M. genitalium infection (OR 0.8; 95% CI 0.6-1.0) 9 . Another study of 409 MSM in Shenzhen, China, reported that condomless penile-anal intercourse in the past six months had higher odds of acquiring urethral M. genitalium infection (OR 4.8; 95% CI 1.4-16.5) 11 . These studies did not include all potential such as oral sex, rimming or kissing on the transmission of M. genitalium despite these practices having been shown to transmit other bacterial STIs such as Neisseria gonorrhoeae and Chlamydia trachomatis 12,13 . Mathematical models can investigate different transmission routes and the plausibility of transmission between different anatomical sites, particularly when the transmission may be complex or difficult to study epidemiologically 13,14 . Investigating the potential role of different sexual practices for the transmission of M. genitalium in MSM using epidemiological studies is difficult because many sexual practices occur together in the same sexual encounter necessitating large numbers in studies to separate the role of each sexual practice 15 . For example, kissing, oral sex, riming, and anal sex more often occur together and are so correlated that it is virtually impossible to look at the independent contribution of different practices either statistically or through simple stratifications 16 .
We and others have created anatomical site-specific mathematical models in Neisseria gonorrhoeae [17][18][19] and Chlamydia trachomatis 15 , but no mathematical models have explored the transmission of M. genitalium in MSM. A few mathematical models have been published in heterosexuals 20,21 , although none of these studies used anatomical site-specific models. We aimed to develop a series of anatomical site-specific mathematical models to determine what sexual practices were necessary to replicate single-site infection of M. genitalium at the oropharynx, anorectum and urethra and multi-site infections.

Results
Calibration of M. genitalium transmission model. Figure 1 shows the model's outputs, including estimates of the simulated prevalence of single-site and multi-site infection at the oropharynx, urethra and anorectum. Model 1 (transmission by only penile-anal sex and penile-oral sex) was able to fit the empirical prevalence data of single-site and multi-site infection at the oropharynx, urethra and anorectum (Fig. 1). When we added rimming, kissing or both to model 1 (models 2-4), we could also fit the empirical prevalence data of single-site and multi-site infection at the oropharynx, urethra and anorectum (Fig. 1).
To select the best-fitting model, we evaluated the models by generating their sum of squared errors (SSE) and compared the results of models 2-4 to model 1. Model 2 (addition of rimming only) and model 4 (addition of both rimming and kissing) demonstrated a significantly higher error in calibration to empirical data than model 1 (model 2 with an SSE of 11.51 × 10 -6 [95% CI 3.57 × 10 -6 -14.77 × 10 -6 ] vs. model 1 with an SSE of 6.43 × 10 -6   Table S1). The model estimated anatomical per-act transmissibility was provided in the supplementary materials ( Supplementary Fig. S1).
Using calibrated models to estimate the incidence of M. genitalium. We used model 1 (our bestfitting model) to explore the estimated incidence at different anatomical sites (oropharynx, urethra and anorectum) or the contribution that different sexual practices made to incident M. genitalium infection. Model 1 estimated that anorectal infection accounted for 61.8% of incident cases, urethral infection for 34.8% and oropharyngeal infection for 3.4% of incident cases. The proportion of incident infections that occurred at the oropharynx, anorectum or urethra in the four models is shown in Fig. 2a. We also provided person-years incidence at the oropharynx, anorectum or urethra in the supplementary materials. (Supplementary Table S2).
To explore the relative importance of sexual practices for new M. genitalium infection, we estimated the proportion of incident infections due to specific sexual practices in the four models, and this is shown in Fig. 2b. Our best model (Model 1) estimated that the proportion of incident M. genitalium infections due to penile-anal sex only was 82.4%, and penile-oral sex only was 17.6%. Even in the models that included riming and kissing, only a relatively small proportion of cases were due to these sexual practices, with kissing responsible for only 1.6-1.9% of cases (Model 3 and 4).

Sensitivity analysis. We performed sensitivity analyses on model 1 (oral and anal sex only). The results
showed that varying key model parameters (duration of infection and frequency of sexual practices) did not alter our conclusions. Model 1 still reliably replicated single-site and multi-site infections at the oropharynx, urethra, and anorectum ( Supplementary Fig. S2). Furthermore, our sensitivity analyses did not significantly change the proportion of incident infections that occurred at the oropharynx (1.8-3.6%), anorectum (61.5-68.8%) or urethra (28.7-35.1%). (Supplementary Fig. S3a). Our sensitivity analyses did not significantly change the propor- www.nature.com/scientificreports/ tion of incident infections due to penile-anal sex only was 84.0-86.9% and penile-oral sex only was 13.1-16.0%.

Discussion
Our model is the first model to explore the role that different sexual practices play in transmitting M. genitalium to different anatomical sites in MSM. Our findings suggest that oral and anal sex alone can explain the M. genitalium prevalence data at the oropharynx, urethra, and rectum (either alone or in combination) without the need to invoke transmission by kissing or rimming. The inclusion of rimming or kissing did not substantially improve our model's calibration that included only anal sex and oral sex. Our model also demonstrates that the anorectum is the most important site, followed by the urethra and that the oropharynx is relatively unimportant in the transmission of M. genitalium between men. Our model shows that penile-anal sex is the main contributor to new M. genitalium infections. Our findings suggest that effective prevention measures to control M. genitalium infection will need to reduce transmission by penile-anal sex, accounting for more than 80% of incident cases.
Our results indicate that oral sex may be responsible for 18% of new infection cases in MSM. Our study needs to be confirmed in epidemiological studies, but our findings could provide some guidance for the future direction of M. genitalium studies.
Our findings suggest that incident M. genitalium infection is uncommon and that oropharyngeal infection may be due to penile-oral sex. We estimated that only 3.4% of incident M. genitalium infection occurred at the oropharynx. Our findings may help explain the observation that oropharyngeal M. genitalium infection is not common in MSM 1,9 . Our results may suggest that new oropharyngeal infection (3.4%) arises from urethral infection through penile-oral sex (from the urethra to oropharynx) and probably not from kissing. The estimated incidence of oropharyngeal infection is substantially lower than anal infection, consistent with oropharyngeal infection being uncommon in MSM 9,10,22 . Nevertheless, we estimate that about 40.8% (14.2%/34.8%) of new urethral infections could result from oral sex.
We also investigated the role of that oropharyngeal M. genitalium infection could potentially play if it were transmitted by other sexual practices other than oral sex. While models 2-4 were either more or not different from model 1, we found that between 1.7% (model 4) to 2.4% (model 2) of new oropharyngeal infection may arise from anal infection through rimming (from anorectum to oropharynx). Our model also predicted that between 1.6% (model 4) to 1.9% (model 3) of new oropharyngeal infection might arise from anal infection through kissing (from the oropharynx to oropharynx). Future empirical studies will be needed to confirm or refute the findings of our models.
Our study suggests that new M. genitalium infection mainly occurs at the anorectum and urethra, with 61.8% of incident cases occurring at the anorectum and 34.8% at the urethra (model 1). Our best model (model 1) also estimated that insertive penile-anal sex contributed significantly more to new infection than receptive anal sex (61.8% vs. 20.6%). Thus, preventing transmission from condomless anal sex, particularly insertive penile-anal sex, is important for preventing M. genitalium infection at the urethra or anorectum in MSM 11,23 . Under this context, we hope our work could encourage further empirical research to explore our estimates for the prevention of M. genitalium through condomless anal sex.
This study has some limitations. First, there were limited publications on the epidemiology of M. genitalium site-specific infection in MSM to test our models, which meant we used only three studies to calibrate our models. The proportion of MSM who had multi-site infections of M. genitalium was relatively low in all three studies, and therefore our estimate has wide confidence intervals. We calibrated our model to the weighted average of the prevalence to narrow confidence intervals for precise model calibration. Second, we had to make some assumptions about the parameters when published data was not available. For example, the natural history parameters for M. genitalium were particularly uncertain 20 , and little is known about the natural history of untreated infection 24 . We, therefore, assumed some parameters for M. genitalium because the natural history of M. genitalium is analogous to chlamydia 25 . Uncertainties in the proportion of asymptomatic urethral infection and bacterial load at various anatomical sites may affect the estimate of transmission 17 . To address this issue, we performed uncertainty and sensitivity analysis. Our sensitivity analyses showed that varying key model outcome indicators (duration of infection and frequency of sexual practices) did not alter our conclusions related to M. genitalium model calibration and incidence estimation. Moreover, there may be other sexual practices that we did not consider in our M. genitalium model.  (Fig. 3).

Methods
In our baseline model, we included oral sex and anal sex because both have been shown to play a role in the transmission of gonorrhoea and chlamydia 12,27,28 . We then built other models by progressively adding sexual practices, such as kissing and rimming that have been shown to play a role in transmission in other STIs 12,13 , to determine what sexual practices best replicated the observed prevalence at each anatomical site (Fig. 3).
Our M. genitalium models included the following assumptions: (1) M. genitalium multi-site infection could develop in a man who is already infected at one anatomical site when he has sex with another infected partner; www.nature.com/scientificreports/ and (2) oropharyngeal infection attributed to sexual practices involved oropharynx site such as oral sex, rimming, and kissing.

Model development.
We established four compartmental models to test the effect of different sexual practices on the transmission of M. genitalium (outlined in Fig. 3). These transmission routes included: (a) penileanal sex and penile-oral sex; (b) penile-anal sex and penile oral sex and oral-anal sex (rimming); (c) penile-anal sex and penile-oral sex and kissing; and (d) penile-anal sex and penile-oral sex and rimming and kissing. The sexual practices simulated in models 1 to 4 were demonstrated in Fig. 1. The M. genitalium models (models 1-4) were represented as a group of ordinary differential equations (Supplementary Table S1).

Data sources and model parameters.
Our model parameters were collected from previously published biological and behavioural data of M. genitalium (Supplementary Table S2). Unlike Neisseria gonorrhoeae and Chlamydia trachomatis, international guidelines do not recommend screening for M. genitalium at any site 1 . A recent study concluded that offering screening for M. genitalium to MSM could slightly reduce the prevalence and incidence but also substantially increase the selection of macrolide resistance 29 . Therefore, we did not include screening in our models. The detailed calibration procedures were provided in the Supplementary Information. We calibrated the model to the prevalence of M. genitalium infections. Based on a previous systematic review and meta-analysis findings, we knew that M. genitalium was uncommonly detected in the oropharynx 1 . The meta-analysis collected data of oropharyngeal M. genitalium from seven studies. We excluded two studies from conference abstracts because of the inadequate description of the study methods. Among the remaining five studies, one study reported the required information stratified by anatomical sites 9 . Then we contacted authors from the other four studies, and two responded to us with data with stratification of multi-site infection 10,22 .

Model calibration and model outputs.
The two key model outputs included model-estimated prevalence and incidence. We sampled the parameter space using Latin Hypercube Sampling (LHS) based on the ranges of our input parameters. We simulated 300 parameter sets using LHS as the initial points for calibration. For each set, we simulated the transmission to obtain the equilibrium prevalence at single-site infection (infection at the oropharynx only, infection at the urethra only, infection at the anorectum only), and multi-site infection (infection at both oropharynx and urethra, infection at both oropharynx and anorectum, infection at both urethra and anorectum, and infection at all three anatomical sites). We measured the calibration error by calculating the sum of squared error between the empirical infection data and the corresponding modelsimulated results. We used fmincon, a MATLAB routine that employed a 'trust-region-reflective' optimisation approach, to minimise the sum of squared error (SSE) for each of the 300 simulations 30 . Out of these simulations, we sorted the simulation outputs in the descending order of SSE. The top 10% of simulations with the least SSE were regarded were used to generate the 95% confidence intervals of the model outputs. We used an independent-samples t-test to examine the differences in the SSE between two models 15,19 . Statistical significance was considered at p < 0.05. All analyses were conducted in MATLAB R2019a. The model parameters, model calibration process have been described in detail in the Supplementary S2. We used the calibrated models to estimate M. Genitalium incidence. In brief, we estimated the new M. Genitalium infections at any given time and calculated the ratio between the number of new infections and the number of susceptible men. The study methods have been reported previously 15,17,19 . We assessed the relative incidence (proportion of incidence cases) based on person-years incidence to explore the relative importance of different anatomical sites (oropharynx, urethra and anorectum) or different sexual practices. We calculated the relative incidence as the rate of incidence cases by different anatomical sites (oropharynx, urethra and anorectum) or sexual practices (numerators) and the sum of all M. Genitalium cases in a year (denominator).
Uncertainty and sensitivity analysis. Several natural history parameters of M. genitalium were uncertain (e.g. duration of infection) 20,31 , and so is the frequency of sexual practices in MSM 17 . To evaluate the stability of our results to uncertainty, we conducted sensitivity analyses on the M. genitalium models by varying duration of infection (reduced to half the duration of asymptomatic oropharyngeal and anal infection) and frequency of sexual practices (increased to double or half the days of sexual practices including anal sex and oral sex).