Modelling the impact of correlations between condom use and sexual contact pattern on the dynamics of sexually transmitted infections

Modelling the impact of correlations between condom use and sexual contact pattern on the... Background: It is believed that sexually active people, i.e. people having multiple or concurrent sexual partners, are at a high risk of sexually transmitted infections (STI), but they are likely to be more aware of the risk and may exhibit greater fraction of the use of condom. The purpose of the present study is to examine the correlation between condom use and sexual contact pattern and clarify its impact on the transmission dynamics of STIs using a mathematical model. Methods: The definition of sexual contact pattern can be broad, but we focus on two specific aspects: (i) type of partnership (i.e. steady or casual partnership) and (ii) existence of concurrency (i.e. with single or multiple partners). Systematic review and meta-analysis of published studies are performed, analysing literature that epidemiologically examined the relationship between condom use and sexual contact pattern. Subsequently, we employ an epidemiological model and compute the reproduction number that accounts for with and without concurrency so that the corresponding coverage of condom use and its correlation with existence of concurrency can be explicitly investigated using the mathematical model. Combining the model with parameters estimated from the meta-analysis along with other assumed parameters, the impact of varying the proportion of population with multiple partners on the reproduction number is examined. Results: Based on systematic review, we show that a greater number of people used condoms during sexual contact with casual partners than with steady partners. Furthermore, people with multiple partners use condoms more frequently than people with a single partner alone. Our mathematical model revealed a positive relationship between the effective reproduction number and the proportion of people with multiple partners. Nevertheless, the association was reversed to be negative by employing a slightly greater value of the relative risk of condom use for people with multiple partners than that empirically estimated. Conclusions: Depending on the correlation between condom use and the existence of concurrency, association between the proportion of people with multiple partners and the reproduction number can be reversed, suggesting the sexually active population is not necessary a primary target population to encourage condom use (i.e., sexually less active individuals could equivalently be a target in some cases). Keywords: Unprotected sex, Partnership, Condom, HIV, Gonorrhoea, Chlamydia * Correspondence: nishiurah@med.hokudai.ac.jp Graduate School of Medicine, Hokkaido University, Hokkaido, Japan CREST, Japan Science and Technology Agency, Saitama, Japan Full list of author information is available at the end of the article © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 2 of 9 Background can be broad, but we focus on two specific aspects: (i) type Sexually transmitted infection (STI) remains to be a of partnership (steady or casual) and (ii) existence of con- serious concern of public health, involving more than currency (single or multiple partners).Wehavetonote that 30 pathogens [1, 2]. Of these, major eight STIs include the type of partnership characterizes the relationship of a syphilis, gonorrhoea, chlamydia, trichomoniasis, hepa- particular couple experiencing a sexual contact, whereas titis B virus infection, herpes simplex virus infection, the existence of concurrency purely dictates the number of human immunodeficiency virus (HIV) infection, and sexualcontact during thesametimeperiod. Forexample, human papilloma virus infection (HPV), that are mainly one can have two concurrent partners, one partnership is linked to sexual contact. Given that one cannot fully steady and the other is causal. Second, if the number of rely on treatment of these diseases, it is vital that preven- contact is associated with condom use, we investigate tion should be the main stream of interventions. Indeed, which (single vs. multiple) is more likely to contribute to even among curable STIs, acute course of infection can the transmission at a population level, employing a math- sometimes develop to urethritis, cervicitis, genital ulcer- ematical model that captures the transmission dynamics. ation and pelvic inflammatory disease (PID) [3]. The PID caused by Chlamydia trachomatis infection can result in Methods multitudes of adverse pregnancy outcomes including mis- The present study is composed of two major analytic carriage [4, 5]. Moreover, bacterial STIs including syphilis steps, i.e. (i) a systematic review of literature and (ii) a and chlamydia are known to be associated with elevated mathematical modelling of the transmission dynamics. risk of HIV infection [6]. Without any doubt, the mainstream of STI prevention is to use the male latex condom. While the condom was Search strategy originally invented as one of contraceptive options, its Studies containing data on the correlation between con- prophylactic use has been shown to be useful through dom use and sexual contact pattern were retrieved from the epidemic of HIV/AIDS and protective efficacy of the MEDLINE (PubMed) and Web of Science electronic latex condom have been demonstrated for a variety of databases on 24 April 2016. We used the following free STI pathogens [7]. The condom is nowadays in the text search terms in “All fields”: World Health Organization’s list of essential medicines needed in the social system. While numerous studies #1: “condom use” OR “safer sex” OR “unprotected took place on the preventive use of condom including intercourse” OR “unprotected sex” OR “unsafe sex” its proper use, one of main concerns has been whether a #2: partner OR partners OR partnership partner at risk actually employs this sheath-shaped bar- #3: prospective OR cohort rier device during the potentially unsafe sexual contact. #4: gay[TI] OR homosexual[TI] OR homosexuals[TI] Who should then wear the condom during sexual con- OR lesbian[TI] OR “men who have sex with men”[TI] tact? Among non-experts, there has been a misconception OR MSM[TI] that only people who have multiple partners should use #5: “injecting drug user” OR “injecting drug users” OR condom [8]. Considering the frequency and diversity of “injection drug use” OR “injection drug users” OR IDU sexual contact that sexually active individuals experience, #6: #1 AND #2 AND #3 NOT #4 NOT #5 wearing condom among people with multiple partners might be a reasonable advice. Nevertheless, it could also be We have limited research studies to only those de- true that people with more sexual partners generally are signed as prospective or cohort studies, because relative more aware of the importance of prevention such as utiliz- risk estimate has been sought to calculate the excess risk ing condoms [9], and awareness of those with a steady part- of concurrent partnership for not using condom. ner may not be as high as those with casual partners. No systematic review of prospective studies has taken place to examine the relationship between condom use and sexual contact pattern, such as type of partnership or the existence Study selection of concurrency. The systematic search of literature was conducted from The purpose of the present study is to examine the July 2014 to April 2016. All titles identified by the search correlation between condom use and sexual contact pat- strategy were independently screened by two authors tern and clarify its impact on the transmission dynamics (N.Y. and K.E.). Abstracts of potentially relevant titles of STIs using a mathematical model. Our task is twofold. were then reviewed for eligibility, and appropriate arti- First, we examine whether sexual contact pattern is asso- cles were selected for closer examination if any descrip- ciated with frequency of condom use through systematic tion of correlation between condom use and sexual review and meta-analysis. The definition of contact pattern contact pattern was given. Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 3 of 9 Systematic review generated by a single typical infectious individual in a fully Although sexual contact pattern can be broadly interpreted susceptible population, which acts as the threshold of ob- and defined in various ways, we focus on two specific as- serving a major epidemic. To compute K, each element of pects as explanatory variables: (i) whether the partnerships the contact matrix is parameterized as follows: were steady or casual and (ii) whether the persons had a sin- pw gleormultiple(concurrent)partnersatthesametime.Our c ¼ wc θ þðÞ 1−θ ; ð2Þ m f pw þðÞ 1−p dichotomous outcome variable is the use of condom. The risk of using condom was calculated as the proportion of 1−p c ¼ wcðÞ 1−θ ; ð3Þ identified condom use partnership (or persons) divided by m f pw þðÞ 1−p the total number of a particular type of partnership (or per- pw sons). Then, the relative risk of using condom given a type c ¼ cðÞ 1−θ ; ð4Þ m f pw þðÞ 1−p of partnership (or person) was estimated for each extracted study, followed by meta-analysis. Statistical heterogeneity 1−p was assessed by Cochran’sQandI statistic which represent c ¼ c θ þðÞ 1−θ ; ð5Þ m f pw þðÞ 1−p the extent of the degree of variation between studies [10, 11]. All statistical data were analysed using a statistical pw c ¼ wc θ þðÞ 1−θ ; ð6Þ software R version 3.1.2 (R Core Team, Vienna, Austria, f m pw þðÞ 1−p 2017) and the library ‘metafor’ was used for forest plot. 1−p c ¼ wcðÞ 1−θ ; ð7Þ f m Epidemic model with populations with or without pw þðÞ 1−p concurrency (with a single or multiple partners) pw Using the estimated association between condom use c ¼ cðÞ 1−θ ; ð8Þ f m pw þðÞ 1−p and sexual contact pattern, we examine its role in deter- mining the transmission dynamics of STI. Considering 1−p c ¼ c θ þðÞ 1−θ ; ð9Þ f m the heterogeneous sexual contact pattern, both the num- 2 pw þðÞ 1−p ber of sexual partners and the types of partnership (i.e., steady or casual) would play key roles in modulating the where c is the contact rate of people with a single partner epidemic dynamics. However, hereafter, we focus on only, and w scales the relative contact rate of people with modelling concurrency. The population is divided into multiple partners as compared with single partner only. The four groups due to two sex (i.e., male and female) and parameter θ is referred to as the assortativity coefficient, two different categories with a single or multiple part- which describes the proportion of contacts that are spent ners. The epidemic dynamics of STI is described by the within the same group [12]. Thus, (1-θ) of the contacts are following next generation matrix (NGM), K: spent randomly, or in the above formulation, that is equiva- lent to say proportional to relative population size of each 2 3 c c group to be used as the weight. In the extreme case, θ=0 m f m f 1 1 1 2 6 7 0 c c and 1 corresponds to the random mixing and fully assorta- m f m f 2 2 1 2 6 7 KC¼ ð1Þ 4 5 c c 0 tive mixing (i.e. contacts occur only in the same groups), f m f m 1 2 1 1 c c respectively. For example, sexual contact rate of a female f m f m 2 1 2 2 with multiple partners (f ) with a male with multiple part- pw where C stands for the contact matrix, composed of the ners (m ), C , is described as wcfθ þð1−θÞ g, m f 1 1 1 pwþð1−pÞ contact rate per unit time within and between different because, among the total of contact, wc, the proportion θ is groups of people. That is, the element c represents the rate distributed to the contacts withmalewithmultiplepartners, ij of sexual contact that one individual in group j experiences and the rest of total contact rate, (1-θ) is randomly distrib- with partner(s) in the group i.Subscripts m and f repre- uted to the contacts with male with or without concurrency. i i sents male and female groups with a single or multiple p is theproportionof peoplewithmultiplepartnersamong sexual partners i, i.e., i = 1 representing population with the entire population, and the complement (1-p) describes multiple partners and 2 with a single partner. For simplicity, the proportion of people with a single partner only. we ignore the issue of homosexual transmission in this Adding onto the abovementioned model, we account model. Assuming that there would be no biological differ- for the condom use. Assuming that condoms can per- ence among groups with respect to infectiousness, suscepti- fectly prevent infection, the proportion of condom users bility and the incubation period, the next generation depends only on the existence of concurrency (i.e. with a matrix, K is assumed as proportional to the contact matrix, single or multiple partners). Not only male, but hereafter C.The eigenvalue of K would yield the basic reproduction we consider that an identical impact is seen in female as number, R , i.e., the average number of secondary cases well. The NGM under intervention, K′ is described as 0 Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 4 of 9 2 3 ðÞ 1−qπ k ðÞ 1−qπðÞ 1−π k m f m f 1 1 1 2 6 2 7 0 01ðÞ −qπðÞ 1−π k ðÞ 1−π k 6 7 m f m f 2 1 2 2 K ¼ ; ð10Þ 6 7 4 ðÞ 1−qπ k ðÞ 1−qπðÞ 1−π k 5 f m f m 1 2 1 1 ðÞ 1−qπðÞ 1−π k ðÞ 1−π k 0 f m f m 1 2 2 2 where k represents the (i,j)-th element of the next gen- of the effective reproduction number to proportion of ij eration matrix K in the absence of intervention, and π people with multiple sexual partners (p). The set of as- represents the coverage of condom use among people sumed parameters is shown in the Table 1. with multiple partners. q is the relative coverage of con- dom use among the people with a single partner alone. Ethical considerations In each element with q and π, π appears twice, because The present study analysed only published articles and condom use can perfectly prevent infection, risky sexual handled openly available data. As such, the present study intercourse happens only between non-condom males did not require ethical approval. and non-condom use females (Fig. 1). As an example, 0 0 the illustration of K ðK Þ is shown in Fig. 1. This Results 4;2 f ;m Systematic review element describes the transmission from men with a We retrieved 1558 potential publications based on two dif- single partner to women with a single partner. The pro- ferent databases (Fig. 2), of which 259 were considered portion of population with condom use is π for each potentially eligible for assessing the abstract. Of 1299 population, contacts involving at least one condom user excluded studies, 576 appeared to be duplicates (i.e. hit on (grey shaded parts) are excluded from the transmission both databases), 9 were not in English, and 714 were deter- dynamics. Thus the element is composed of only the mined to be irrelevant subject. Reading abstracts, 172 titles transmission between non-condom users. We can com- were excluded because they were regarded as irrelevant to pute the largest eigenvalue of K′ that yields the effective our research subject. Reviewing the full text, another 70 reproduction number. studies were excluded as 46 did not include information re- garding correlation between condom use and partnership, Scenario analysis and it was hard to extract the data from 10 studies, the To investigate the relationship between epidemiological research design did not meet our criteria in 6 articles, and dynamics and concurrency, we examined the sensitivity 10 articles only focused on particular risk groups such as commercial sex workers or intravenous drug users. Finally, 15 studies were determined to be eligible and included in this systematic review [9, 13–26]. Of the included 15 stud- ies, a total of 12 studies described the association between condom use and having steady partner (or casual part- ner(s)). Of the 15 studies, 5 studies described the associ- ation between condom use and concurrency (i.e. single partner alone or multiple partners). Figure 3 summarizes the characteristics of the selected 12 different studies on the type of partnerships. There was variation in literary expression to define the type of partner- ship. We define the use of following words as the signature of steady partner: (i) boyfriend/girlfriend, (ii) main, (iii) rela- tionship partner, (iv) regular and (v) primary. Conversely, we define the use of following terms as casual: (i) one-time, (ii) non-regular, (iii) secondary and (iv) short-term. With re- spect to the use of condom, its use was quantified in differ- Fig. 1 Example of the construction of next generation matrix. Based on the next generation matrix without any intervention, K, next ent manner by different studies. In five of the included generation matrix with condo use, K′ was constructed. As an studies, data were collected and classified as non-yes-or-no 0 0 example, the illustration of K ð¼ K Þ is shown. This element 4;2 f ;m 2 2 responses in a categorical manner such as “never”, “occa- describes the transmission from men with a single partner to sionally/often” or “always”. Because seven studies show only women with a single partner dichotomized data with yes or no responses, categories Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 5 of 9 Table 1 Parameters for sensitivity analysis of the sexual transmitted infection Parameters Description Assumed values R Basic reproduction number 3.65 [33] c Rate of sexual contact among people with steady (or single) partner only Back-calculated from R w Relative frequency of sexual contact among people with casual (or multiple) partners 4.0 (Assumed) π Coverage of condom use 0.49 (Estimated in systematic review) q Relative coverage of condom use among people with multiple partners 1.32 (Estimated in systematic review) p Proportion of people with multiple partners 0.30 (Assumed) θ Assortativity coefficient (i.e., proportion of contacts that are spent for within group mixing) 0.20 (Assumed) indicating any degree of condom use (e.g. “sometimes” or Figure 4 summarizes the characteristics of the se- “always”) are presented as yes as opposed to non-existent lected 5 studies on concurrency. The relative risk of condom use (e.g. “never” or “none”) with the results pre- using condom given multiple partners was signifi- sented as “condom use” or “condom non-use” to ensure cantly greater than the value of 1 in 3 published stud- the consistency. ies. None of the included studies indicated that those The relative risk of using condom given casual part- with multiple partners less frequently used condom. nership was significantly greater than the value of 1 in 7 Weighted mean of the relative risk based on random published studies. Only 1 study in Europe indicated that effects model was estimated at 1.3 (95% confidence those with casual partners less frequently used condom. interval (CI): 1.2, 1.5). If a fixed effects model was Weighted mean of the relative risk based on random ef- employed, the weighted mean was estimated at 1.5 fects model was estimated at 1.2 (95% confidence inter- (detailed Results not shown). Heterogeneity was again val (CI): 0.9, 1.5). Heterogeneity was identified to be identified to be high with I value estimated at 68.8% high with I value estimated at 98.6%. from random effects model. Fig. 2 Flow diagram of study selection. Among a total of 784 and 774 records identified by using MEDLINE and Web of Science, respectively, a total of 15 studies fulfilled inclusion criteria and were included in our systematic review Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 6 of 9 Fig. 3 Forest plot of potential association between condom use and partner type (i.e., steady or casual). Centre of each square points the relative risk with its size reflecting the sample size. Whiskers extend to lower and upper 95% confidence intervals. The right arrow in the Tanzania study indicates that the upper bound is greater than upper limit of our horizontal axis scale. Diamond represents the group estimate based on random effects model. I statistic shows the extent of heterogeneity Fig. 4 Forest plot of potential association between condom use and concurrency (i.e., having 1 partner alone or 2 or more concurrent partners). Centre of each square points the relative risk with its size reflecting the sample size. Whiskers extend to lower and upper 95% confidence intervals. Diamond represents the group estimate based on random effects model. I statistic shows the extent of heterogeneity Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 7 of 9 Fig. 5 Sensitivity of the transmissibility to the fraction of people with multiple sexual partners. Different lines represent the estimate of transmissibility (effective reproduction number) with different values of q, the relative risk of condom use due to more active sexual partnership. The value of 1.32, 1.48 and 1.51 were derived from systematic review and 1.60 is what the authors assumed Epidemiological modelling transmission dynamics (especially, the relative risk q Based on the relative risk of condom use given multiple and perhaps also the relative contact frequency w and partners, the effect size was estimated at 1.32 or 1.48 assortativity θ), the resulting positivity of the relation- using random effects or fixed effect models, respectively. ship between the reproduction number and the propor- Among included studies, the greatest effect size by pub- tion of people with multiple partners is determined. lished study was 1.51. In addition to these values, we exam- ined another bigger effect size at 1.60. Consequently, we Discussion examined the sensitivity of effective reproduction number The present study analysed the correlation between to the proportion of the multiple partnership in the popula- condom use and type of partnership or concurrency by tion using the fixed values of q at 1.32, 1.48, 1.51 and 1.60 conducting systematic review of published literature. (Fig. 5). Using the published realistic values of q (i.e., 1.32), Subsequently, the impact of the correlation between the effective reproduction number increased if the propor- condom use and concurrency on the transmission dynam- tion of people with multiple partners (p) was elevated. This ics was examined computing the effective reproduction was also the case for q = 1.48 and 1.51, but the extent of number and using empirically estimated relative risk of increase was almost diminished. condom use among people with multiple partners. Empir- However, if q is as high as 1.60, the relationship between ical datasets indicated that a greater number of people used the effective reproduction number and proportion of condoms during sexual contact outside of an ongoing rela- people with multiple partners was reversed, i.e., as tionship (casual contact) than with a steady partner. people become more likely to have multiple partners, Furthermore, people with multiple partners use con- the reproduction number takes smaller value. That is, doms more frequently than people with a single part- depending on parameters that govern the sexual ner alone. Embedding the empirical estimate onto the Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 8 of 9 mathematical model, a positive relationship between association may be reversed, and then, it may be more the reproduction number and the proportion of people beneficial to target people with steady or single partner with multiple partners was identified. Nevertheless, the alone. In other words, depending on the correlation be- relationship was reversed to be negative by employing tween condom use and type of partnership or concur- a greater value of the relative risk of condom use given rency, theoretically supported type of people to be multiple partners than that empirically estimated. intervened may likely vary. The present study under- In foregoing studies of STI modelling, there has been scores the need to explore the correlation in a variety a trend to focus on partnership via risk-based modelling of settings, e.g. in a closely related group of people in- approach incorporating contact frequency to constitute cluding high schools or Universities, or a setting that fo- host type [27] and also employing the so-called pair for- cuses on contact between commercial sex workers and mation modelling approaches [28–31]. There are several males. studies in which sexual behaviour and condom use was Considering that our study rested on a simplistic model, modelled and their association with disease spread dy- three limitations must be noted. First, our model did not namics was examined. Most of those published studies rest on very specific disease in mind. For instance, if we treated sexual behaviour and condom use independently. handle man-to-man transmissible STI, we must have Azizi et al. [32] is similar to ours as they incorporated accounted for men having sex with men (or homosexual correlation between condom use and heterogeneous risk population). We ignored this matter for the simple expos- behaviour. In contrast, we focused only on two specific ition of our theoretical finding. Second, we did not model aspects of sexual behaviour, i.e., type of partnership and and examine the type of partnership (casual and steady concurrency. Especially in the modelling part, we modelled partnership) in the mathematical model. Third, whereas concurrency considering differential contact rate (c vs cw). we simplified the sexual contact pattern as single/multiple We did not (or could not) incorporate all aspects of sexual or steady/casual, concurrency and type of partnership behaviour into simplistic model, but our formulation has might be associated somehow. Sexual contact pattern made each component of the model (i.e. parameters) inter- might have been oversimplified to be immediately applied pretable and observable. For example, we can count the to concrete examples of STI. number of sexual contacts, which is modelled as c or cw, Despite these limitations, we believe that the present population with multiple partners can be easily identified, study successfully clarified the critical fact that individuals although this might be self-reported. This is important es- whohavemultiplepartnershipsuse condom more fre- pecially when the results are translated into public health quently than individuals who have single relationship alone. practice or when parameters are estimated for different To consider possible public health countermeasures against populations. STI, it is advised to explore the correlation between con- In case the relative risk q (i.e., relative condom coverage dom use and sexual contact pattern so that the most im- for people with multiple partners) is in the range of the portant target host can be objectively identified. value estimated from systematic review (and assuming that the assumed values were actually the case), the trans- Conclusions missibility at a population level is likely elevated through Depending on the correlation between condom use and the increase of people with multiple partners. However, type of partnership or concurrency, increase of people when the value q was slightly higher than the empirically with multiple partners may sometimes result in decrease estimated range, the reproduction number appeared to in the reproduction number, and theoretically supported decrease with the increased proportion of people with target host to be intervened may likely vary. The present multiple partners. It is striking that we cannot describe study underscores the need to explore the correlation in the transmission potential in relation to concurrency in a a variety of settings, e.g. in a closely related group of monotonic fashion. Depending on parameters and actual people including high schools or Universities. coverage of condom use, it should be remembered that Abbreviations the increase of multiple partners may lead to decreased HIV: Human immunodeficiency virus; HPV: Human papilloma virus; reproduction number. IDU: Intravenous/injection drug users; NGM: Next generation matrix; The resulting take-home message is straightforward. If PID: Pelvic inflammatory disease; STI: Sexually transmitted infection a positive association between the reproduction number Funding and the proportion of people with multiple partners is HN received funding from the Health and Labour Sciences Research Grant the case, public health interventions should be stressed (H28-AIDS-General-001 and H26-AIDS-YoungInvestigator-004), Japan Agency on sexually high risk population with casual or multiple for Medical Research and Development (AMED), Japanese Society for the Promotion of Science (JSPS) KAKENHI (grant numbers 16KT0130, 16 K15356 partners. Nevertheless, if the correlation between condom and 17H04701), and Japan Science and Technology Agency (JST) CREST pro- use and the type or number of sexual partners is actually gram (JPMJCR1413). The funders had no role in study design, data collection greater than that we estimated, the abovementioned and analysis, decision to publish, or preparation of the manuscript. Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 9 of 9 Availability of data and materials 14. Ellen JM, Adler N, Gurvey JE, Millstein SG, Tschann J. Adolescent condom Collected datasets are available as Figures and Tables. use and perceptions of risk for sexually transmitted diseases. Sex Transm Dis. 2002;44:756–62. 15. Evans BA, Bond RA, MacRae KD. Sexual relationships, risk behaviour, and Authors’ contributions condom use in the spread of sexually transmitted infections to heterosexual NY, KE and HN conceived of the study and built up the model. NY and men. Genitourin Med. 1997;73:368–72. KE conducted a systematic review. KE and NY drafted the first version of 16. 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Cambridge: Cambridge University Press. 1996: pp. 215–238. 13. Catania JA, Stone V, Binson D, Dolcini MM. Changes in condom use among heterosexuals in wave 3 of the AMEN survey. J Sex Res. 1995;32(3):193–200. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theoretical Biology and Medical Modelling Springer Journals

Modelling the impact of correlations between condom use and sexual contact pattern on the dynamics of sexually transmitted infections

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Biomedicine; Biomedicine, general; Systems Biology; Physiological, Cellular and Medical Topics; Statistics for Life Sciences, Medicine, Health Sciences; Bioinformatics; Infectious Diseases
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Abstract

Background: It is believed that sexually active people, i.e. people having multiple or concurrent sexual partners, are at a high risk of sexually transmitted infections (STI), but they are likely to be more aware of the risk and may exhibit greater fraction of the use of condom. The purpose of the present study is to examine the correlation between condom use and sexual contact pattern and clarify its impact on the transmission dynamics of STIs using a mathematical model. Methods: The definition of sexual contact pattern can be broad, but we focus on two specific aspects: (i) type of partnership (i.e. steady or casual partnership) and (ii) existence of concurrency (i.e. with single or multiple partners). Systematic review and meta-analysis of published studies are performed, analysing literature that epidemiologically examined the relationship between condom use and sexual contact pattern. Subsequently, we employ an epidemiological model and compute the reproduction number that accounts for with and without concurrency so that the corresponding coverage of condom use and its correlation with existence of concurrency can be explicitly investigated using the mathematical model. Combining the model with parameters estimated from the meta-analysis along with other assumed parameters, the impact of varying the proportion of population with multiple partners on the reproduction number is examined. Results: Based on systematic review, we show that a greater number of people used condoms during sexual contact with casual partners than with steady partners. Furthermore, people with multiple partners use condoms more frequently than people with a single partner alone. Our mathematical model revealed a positive relationship between the effective reproduction number and the proportion of people with multiple partners. Nevertheless, the association was reversed to be negative by employing a slightly greater value of the relative risk of condom use for people with multiple partners than that empirically estimated. Conclusions: Depending on the correlation between condom use and the existence of concurrency, association between the proportion of people with multiple partners and the reproduction number can be reversed, suggesting the sexually active population is not necessary a primary target population to encourage condom use (i.e., sexually less active individuals could equivalently be a target in some cases). Keywords: Unprotected sex, Partnership, Condom, HIV, Gonorrhoea, Chlamydia * Correspondence: nishiurah@med.hokudai.ac.jp Graduate School of Medicine, Hokkaido University, Hokkaido, Japan CREST, Japan Science and Technology Agency, Saitama, Japan Full list of author information is available at the end of the article © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 2 of 9 Background can be broad, but we focus on two specific aspects: (i) type Sexually transmitted infection (STI) remains to be a of partnership (steady or casual) and (ii) existence of con- serious concern of public health, involving more than currency (single or multiple partners).Wehavetonote that 30 pathogens [1, 2]. Of these, major eight STIs include the type of partnership characterizes the relationship of a syphilis, gonorrhoea, chlamydia, trichomoniasis, hepa- particular couple experiencing a sexual contact, whereas titis B virus infection, herpes simplex virus infection, the existence of concurrency purely dictates the number of human immunodeficiency virus (HIV) infection, and sexualcontact during thesametimeperiod. Forexample, human papilloma virus infection (HPV), that are mainly one can have two concurrent partners, one partnership is linked to sexual contact. Given that one cannot fully steady and the other is causal. Second, if the number of rely on treatment of these diseases, it is vital that preven- contact is associated with condom use, we investigate tion should be the main stream of interventions. Indeed, which (single vs. multiple) is more likely to contribute to even among curable STIs, acute course of infection can the transmission at a population level, employing a math- sometimes develop to urethritis, cervicitis, genital ulcer- ematical model that captures the transmission dynamics. ation and pelvic inflammatory disease (PID) [3]. The PID caused by Chlamydia trachomatis infection can result in Methods multitudes of adverse pregnancy outcomes including mis- The present study is composed of two major analytic carriage [4, 5]. Moreover, bacterial STIs including syphilis steps, i.e. (i) a systematic review of literature and (ii) a and chlamydia are known to be associated with elevated mathematical modelling of the transmission dynamics. risk of HIV infection [6]. Without any doubt, the mainstream of STI prevention is to use the male latex condom. While the condom was Search strategy originally invented as one of contraceptive options, its Studies containing data on the correlation between con- prophylactic use has been shown to be useful through dom use and sexual contact pattern were retrieved from the epidemic of HIV/AIDS and protective efficacy of the MEDLINE (PubMed) and Web of Science electronic latex condom have been demonstrated for a variety of databases on 24 April 2016. We used the following free STI pathogens [7]. The condom is nowadays in the text search terms in “All fields”: World Health Organization’s list of essential medicines needed in the social system. While numerous studies #1: “condom use” OR “safer sex” OR “unprotected took place on the preventive use of condom including intercourse” OR “unprotected sex” OR “unsafe sex” its proper use, one of main concerns has been whether a #2: partner OR partners OR partnership partner at risk actually employs this sheath-shaped bar- #3: prospective OR cohort rier device during the potentially unsafe sexual contact. #4: gay[TI] OR homosexual[TI] OR homosexuals[TI] Who should then wear the condom during sexual con- OR lesbian[TI] OR “men who have sex with men”[TI] tact? Among non-experts, there has been a misconception OR MSM[TI] that only people who have multiple partners should use #5: “injecting drug user” OR “injecting drug users” OR condom [8]. Considering the frequency and diversity of “injection drug use” OR “injection drug users” OR IDU sexual contact that sexually active individuals experience, #6: #1 AND #2 AND #3 NOT #4 NOT #5 wearing condom among people with multiple partners might be a reasonable advice. Nevertheless, it could also be We have limited research studies to only those de- true that people with more sexual partners generally are signed as prospective or cohort studies, because relative more aware of the importance of prevention such as utiliz- risk estimate has been sought to calculate the excess risk ing condoms [9], and awareness of those with a steady part- of concurrent partnership for not using condom. ner may not be as high as those with casual partners. No systematic review of prospective studies has taken place to examine the relationship between condom use and sexual contact pattern, such as type of partnership or the existence Study selection of concurrency. The systematic search of literature was conducted from The purpose of the present study is to examine the July 2014 to April 2016. All titles identified by the search correlation between condom use and sexual contact pat- strategy were independently screened by two authors tern and clarify its impact on the transmission dynamics (N.Y. and K.E.). Abstracts of potentially relevant titles of STIs using a mathematical model. Our task is twofold. were then reviewed for eligibility, and appropriate arti- First, we examine whether sexual contact pattern is asso- cles were selected for closer examination if any descrip- ciated with frequency of condom use through systematic tion of correlation between condom use and sexual review and meta-analysis. The definition of contact pattern contact pattern was given. Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 3 of 9 Systematic review generated by a single typical infectious individual in a fully Although sexual contact pattern can be broadly interpreted susceptible population, which acts as the threshold of ob- and defined in various ways, we focus on two specific as- serving a major epidemic. To compute K, each element of pects as explanatory variables: (i) whether the partnerships the contact matrix is parameterized as follows: were steady or casual and (ii) whether the persons had a sin- pw gleormultiple(concurrent)partnersatthesametime.Our c ¼ wc θ þðÞ 1−θ ; ð2Þ m f pw þðÞ 1−p dichotomous outcome variable is the use of condom. The risk of using condom was calculated as the proportion of 1−p c ¼ wcðÞ 1−θ ; ð3Þ identified condom use partnership (or persons) divided by m f pw þðÞ 1−p the total number of a particular type of partnership (or per- pw sons). Then, the relative risk of using condom given a type c ¼ cðÞ 1−θ ; ð4Þ m f pw þðÞ 1−p of partnership (or person) was estimated for each extracted study, followed by meta-analysis. Statistical heterogeneity 1−p was assessed by Cochran’sQandI statistic which represent c ¼ c θ þðÞ 1−θ ; ð5Þ m f pw þðÞ 1−p the extent of the degree of variation between studies [10, 11]. All statistical data were analysed using a statistical pw c ¼ wc θ þðÞ 1−θ ; ð6Þ software R version 3.1.2 (R Core Team, Vienna, Austria, f m pw þðÞ 1−p 2017) and the library ‘metafor’ was used for forest plot. 1−p c ¼ wcðÞ 1−θ ; ð7Þ f m Epidemic model with populations with or without pw þðÞ 1−p concurrency (with a single or multiple partners) pw Using the estimated association between condom use c ¼ cðÞ 1−θ ; ð8Þ f m pw þðÞ 1−p and sexual contact pattern, we examine its role in deter- mining the transmission dynamics of STI. Considering 1−p c ¼ c θ þðÞ 1−θ ; ð9Þ f m the heterogeneous sexual contact pattern, both the num- 2 pw þðÞ 1−p ber of sexual partners and the types of partnership (i.e., steady or casual) would play key roles in modulating the where c is the contact rate of people with a single partner epidemic dynamics. However, hereafter, we focus on only, and w scales the relative contact rate of people with modelling concurrency. The population is divided into multiple partners as compared with single partner only. The four groups due to two sex (i.e., male and female) and parameter θ is referred to as the assortativity coefficient, two different categories with a single or multiple part- which describes the proportion of contacts that are spent ners. The epidemic dynamics of STI is described by the within the same group [12]. Thus, (1-θ) of the contacts are following next generation matrix (NGM), K: spent randomly, or in the above formulation, that is equiva- lent to say proportional to relative population size of each 2 3 c c group to be used as the weight. In the extreme case, θ=0 m f m f 1 1 1 2 6 7 0 c c and 1 corresponds to the random mixing and fully assorta- m f m f 2 2 1 2 6 7 KC¼ ð1Þ 4 5 c c 0 tive mixing (i.e. contacts occur only in the same groups), f m f m 1 2 1 1 c c respectively. For example, sexual contact rate of a female f m f m 2 1 2 2 with multiple partners (f ) with a male with multiple part- pw where C stands for the contact matrix, composed of the ners (m ), C , is described as wcfθ þð1−θÞ g, m f 1 1 1 pwþð1−pÞ contact rate per unit time within and between different because, among the total of contact, wc, the proportion θ is groups of people. That is, the element c represents the rate distributed to the contacts withmalewithmultiplepartners, ij of sexual contact that one individual in group j experiences and the rest of total contact rate, (1-θ) is randomly distrib- with partner(s) in the group i.Subscripts m and f repre- uted to the contacts with male with or without concurrency. i i sents male and female groups with a single or multiple p is theproportionof peoplewithmultiplepartnersamong sexual partners i, i.e., i = 1 representing population with the entire population, and the complement (1-p) describes multiple partners and 2 with a single partner. For simplicity, the proportion of people with a single partner only. we ignore the issue of homosexual transmission in this Adding onto the abovementioned model, we account model. Assuming that there would be no biological differ- for the condom use. Assuming that condoms can per- ence among groups with respect to infectiousness, suscepti- fectly prevent infection, the proportion of condom users bility and the incubation period, the next generation depends only on the existence of concurrency (i.e. with a matrix, K is assumed as proportional to the contact matrix, single or multiple partners). Not only male, but hereafter C.The eigenvalue of K would yield the basic reproduction we consider that an identical impact is seen in female as number, R , i.e., the average number of secondary cases well. The NGM under intervention, K′ is described as 0 Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 4 of 9 2 3 ðÞ 1−qπ k ðÞ 1−qπðÞ 1−π k m f m f 1 1 1 2 6 2 7 0 01ðÞ −qπðÞ 1−π k ðÞ 1−π k 6 7 m f m f 2 1 2 2 K ¼ ; ð10Þ 6 7 4 ðÞ 1−qπ k ðÞ 1−qπðÞ 1−π k 5 f m f m 1 2 1 1 ðÞ 1−qπðÞ 1−π k ðÞ 1−π k 0 f m f m 1 2 2 2 where k represents the (i,j)-th element of the next gen- of the effective reproduction number to proportion of ij eration matrix K in the absence of intervention, and π people with multiple sexual partners (p). The set of as- represents the coverage of condom use among people sumed parameters is shown in the Table 1. with multiple partners. q is the relative coverage of con- dom use among the people with a single partner alone. Ethical considerations In each element with q and π, π appears twice, because The present study analysed only published articles and condom use can perfectly prevent infection, risky sexual handled openly available data. As such, the present study intercourse happens only between non-condom males did not require ethical approval. and non-condom use females (Fig. 1). As an example, 0 0 the illustration of K ðK Þ is shown in Fig. 1. This Results 4;2 f ;m Systematic review element describes the transmission from men with a We retrieved 1558 potential publications based on two dif- single partner to women with a single partner. The pro- ferent databases (Fig. 2), of which 259 were considered portion of population with condom use is π for each potentially eligible for assessing the abstract. Of 1299 population, contacts involving at least one condom user excluded studies, 576 appeared to be duplicates (i.e. hit on (grey shaded parts) are excluded from the transmission both databases), 9 were not in English, and 714 were deter- dynamics. Thus the element is composed of only the mined to be irrelevant subject. Reading abstracts, 172 titles transmission between non-condom users. We can com- were excluded because they were regarded as irrelevant to pute the largest eigenvalue of K′ that yields the effective our research subject. Reviewing the full text, another 70 reproduction number. studies were excluded as 46 did not include information re- garding correlation between condom use and partnership, Scenario analysis and it was hard to extract the data from 10 studies, the To investigate the relationship between epidemiological research design did not meet our criteria in 6 articles, and dynamics and concurrency, we examined the sensitivity 10 articles only focused on particular risk groups such as commercial sex workers or intravenous drug users. Finally, 15 studies were determined to be eligible and included in this systematic review [9, 13–26]. Of the included 15 stud- ies, a total of 12 studies described the association between condom use and having steady partner (or casual part- ner(s)). Of the 15 studies, 5 studies described the associ- ation between condom use and concurrency (i.e. single partner alone or multiple partners). Figure 3 summarizes the characteristics of the selected 12 different studies on the type of partnerships. There was variation in literary expression to define the type of partner- ship. We define the use of following words as the signature of steady partner: (i) boyfriend/girlfriend, (ii) main, (iii) rela- tionship partner, (iv) regular and (v) primary. Conversely, we define the use of following terms as casual: (i) one-time, (ii) non-regular, (iii) secondary and (iv) short-term. With re- spect to the use of condom, its use was quantified in differ- Fig. 1 Example of the construction of next generation matrix. Based on the next generation matrix without any intervention, K, next ent manner by different studies. In five of the included generation matrix with condo use, K′ was constructed. As an studies, data were collected and classified as non-yes-or-no 0 0 example, the illustration of K ð¼ K Þ is shown. This element 4;2 f ;m 2 2 responses in a categorical manner such as “never”, “occa- describes the transmission from men with a single partner to sionally/often” or “always”. Because seven studies show only women with a single partner dichotomized data with yes or no responses, categories Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 5 of 9 Table 1 Parameters for sensitivity analysis of the sexual transmitted infection Parameters Description Assumed values R Basic reproduction number 3.65 [33] c Rate of sexual contact among people with steady (or single) partner only Back-calculated from R w Relative frequency of sexual contact among people with casual (or multiple) partners 4.0 (Assumed) π Coverage of condom use 0.49 (Estimated in systematic review) q Relative coverage of condom use among people with multiple partners 1.32 (Estimated in systematic review) p Proportion of people with multiple partners 0.30 (Assumed) θ Assortativity coefficient (i.e., proportion of contacts that are spent for within group mixing) 0.20 (Assumed) indicating any degree of condom use (e.g. “sometimes” or Figure 4 summarizes the characteristics of the se- “always”) are presented as yes as opposed to non-existent lected 5 studies on concurrency. The relative risk of condom use (e.g. “never” or “none”) with the results pre- using condom given multiple partners was signifi- sented as “condom use” or “condom non-use” to ensure cantly greater than the value of 1 in 3 published stud- the consistency. ies. None of the included studies indicated that those The relative risk of using condom given casual part- with multiple partners less frequently used condom. nership was significantly greater than the value of 1 in 7 Weighted mean of the relative risk based on random published studies. Only 1 study in Europe indicated that effects model was estimated at 1.3 (95% confidence those with casual partners less frequently used condom. interval (CI): 1.2, 1.5). If a fixed effects model was Weighted mean of the relative risk based on random ef- employed, the weighted mean was estimated at 1.5 fects model was estimated at 1.2 (95% confidence inter- (detailed Results not shown). Heterogeneity was again val (CI): 0.9, 1.5). Heterogeneity was identified to be identified to be high with I value estimated at 68.8% high with I value estimated at 98.6%. from random effects model. Fig. 2 Flow diagram of study selection. Among a total of 784 and 774 records identified by using MEDLINE and Web of Science, respectively, a total of 15 studies fulfilled inclusion criteria and were included in our systematic review Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 6 of 9 Fig. 3 Forest plot of potential association between condom use and partner type (i.e., steady or casual). Centre of each square points the relative risk with its size reflecting the sample size. Whiskers extend to lower and upper 95% confidence intervals. The right arrow in the Tanzania study indicates that the upper bound is greater than upper limit of our horizontal axis scale. Diamond represents the group estimate based on random effects model. I statistic shows the extent of heterogeneity Fig. 4 Forest plot of potential association between condom use and concurrency (i.e., having 1 partner alone or 2 or more concurrent partners). Centre of each square points the relative risk with its size reflecting the sample size. Whiskers extend to lower and upper 95% confidence intervals. Diamond represents the group estimate based on random effects model. I statistic shows the extent of heterogeneity Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 7 of 9 Fig. 5 Sensitivity of the transmissibility to the fraction of people with multiple sexual partners. Different lines represent the estimate of transmissibility (effective reproduction number) with different values of q, the relative risk of condom use due to more active sexual partnership. The value of 1.32, 1.48 and 1.51 were derived from systematic review and 1.60 is what the authors assumed Epidemiological modelling transmission dynamics (especially, the relative risk q Based on the relative risk of condom use given multiple and perhaps also the relative contact frequency w and partners, the effect size was estimated at 1.32 or 1.48 assortativity θ), the resulting positivity of the relation- using random effects or fixed effect models, respectively. ship between the reproduction number and the propor- Among included studies, the greatest effect size by pub- tion of people with multiple partners is determined. lished study was 1.51. In addition to these values, we exam- ined another bigger effect size at 1.60. Consequently, we Discussion examined the sensitivity of effective reproduction number The present study analysed the correlation between to the proportion of the multiple partnership in the popula- condom use and type of partnership or concurrency by tion using the fixed values of q at 1.32, 1.48, 1.51 and 1.60 conducting systematic review of published literature. (Fig. 5). Using the published realistic values of q (i.e., 1.32), Subsequently, the impact of the correlation between the effective reproduction number increased if the propor- condom use and concurrency on the transmission dynam- tion of people with multiple partners (p) was elevated. This ics was examined computing the effective reproduction was also the case for q = 1.48 and 1.51, but the extent of number and using empirically estimated relative risk of increase was almost diminished. condom use among people with multiple partners. Empir- However, if q is as high as 1.60, the relationship between ical datasets indicated that a greater number of people used the effective reproduction number and proportion of condoms during sexual contact outside of an ongoing rela- people with multiple partners was reversed, i.e., as tionship (casual contact) than with a steady partner. people become more likely to have multiple partners, Furthermore, people with multiple partners use con- the reproduction number takes smaller value. That is, doms more frequently than people with a single part- depending on parameters that govern the sexual ner alone. Embedding the empirical estimate onto the Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 8 of 9 mathematical model, a positive relationship between association may be reversed, and then, it may be more the reproduction number and the proportion of people beneficial to target people with steady or single partner with multiple partners was identified. Nevertheless, the alone. In other words, depending on the correlation be- relationship was reversed to be negative by employing tween condom use and type of partnership or concur- a greater value of the relative risk of condom use given rency, theoretically supported type of people to be multiple partners than that empirically estimated. intervened may likely vary. The present study under- In foregoing studies of STI modelling, there has been scores the need to explore the correlation in a variety a trend to focus on partnership via risk-based modelling of settings, e.g. in a closely related group of people in- approach incorporating contact frequency to constitute cluding high schools or Universities, or a setting that fo- host type [27] and also employing the so-called pair for- cuses on contact between commercial sex workers and mation modelling approaches [28–31]. There are several males. studies in which sexual behaviour and condom use was Considering that our study rested on a simplistic model, modelled and their association with disease spread dy- three limitations must be noted. First, our model did not namics was examined. Most of those published studies rest on very specific disease in mind. For instance, if we treated sexual behaviour and condom use independently. handle man-to-man transmissible STI, we must have Azizi et al. [32] is similar to ours as they incorporated accounted for men having sex with men (or homosexual correlation between condom use and heterogeneous risk population). We ignored this matter for the simple expos- behaviour. In contrast, we focused only on two specific ition of our theoretical finding. Second, we did not model aspects of sexual behaviour, i.e., type of partnership and and examine the type of partnership (casual and steady concurrency. Especially in the modelling part, we modelled partnership) in the mathematical model. Third, whereas concurrency considering differential contact rate (c vs cw). we simplified the sexual contact pattern as single/multiple We did not (or could not) incorporate all aspects of sexual or steady/casual, concurrency and type of partnership behaviour into simplistic model, but our formulation has might be associated somehow. Sexual contact pattern made each component of the model (i.e. parameters) inter- might have been oversimplified to be immediately applied pretable and observable. For example, we can count the to concrete examples of STI. number of sexual contacts, which is modelled as c or cw, Despite these limitations, we believe that the present population with multiple partners can be easily identified, study successfully clarified the critical fact that individuals although this might be self-reported. This is important es- whohavemultiplepartnershipsuse condom more fre- pecially when the results are translated into public health quently than individuals who have single relationship alone. practice or when parameters are estimated for different To consider possible public health countermeasures against populations. STI, it is advised to explore the correlation between con- In case the relative risk q (i.e., relative condom coverage dom use and sexual contact pattern so that the most im- for people with multiple partners) is in the range of the portant target host can be objectively identified. value estimated from systematic review (and assuming that the assumed values were actually the case), the trans- Conclusions missibility at a population level is likely elevated through Depending on the correlation between condom use and the increase of people with multiple partners. However, type of partnership or concurrency, increase of people when the value q was slightly higher than the empirically with multiple partners may sometimes result in decrease estimated range, the reproduction number appeared to in the reproduction number, and theoretically supported decrease with the increased proportion of people with target host to be intervened may likely vary. The present multiple partners. It is striking that we cannot describe study underscores the need to explore the correlation in the transmission potential in relation to concurrency in a a variety of settings, e.g. in a closely related group of monotonic fashion. Depending on parameters and actual people including high schools or Universities. coverage of condom use, it should be remembered that Abbreviations the increase of multiple partners may lead to decreased HIV: Human immunodeficiency virus; HPV: Human papilloma virus; reproduction number. IDU: Intravenous/injection drug users; NGM: Next generation matrix; The resulting take-home message is straightforward. If PID: Pelvic inflammatory disease; STI: Sexually transmitted infection a positive association between the reproduction number Funding and the proportion of people with multiple partners is HN received funding from the Health and Labour Sciences Research Grant the case, public health interventions should be stressed (H28-AIDS-General-001 and H26-AIDS-YoungInvestigator-004), Japan Agency on sexually high risk population with casual or multiple for Medical Research and Development (AMED), Japanese Society for the Promotion of Science (JSPS) KAKENHI (grant numbers 16KT0130, 16 K15356 partners. Nevertheless, if the correlation between condom and 17H04701), and Japan Science and Technology Agency (JST) CREST pro- use and the type or number of sexual partners is actually gram (JPMJCR1413). The funders had no role in study design, data collection greater than that we estimated, the abovementioned and analysis, decision to publish, or preparation of the manuscript. Yamamoto et al. Theoretical Biology and Medical Modelling (2018) 15:6 Page 9 of 9 Availability of data and materials 14. Ellen JM, Adler N, Gurvey JE, Millstein SG, Tschann J. Adolescent condom Collected datasets are available as Figures and Tables. use and perceptions of risk for sexually transmitted diseases. Sex Transm Dis. 2002;44:756–62. 15. Evans BA, Bond RA, MacRae KD. Sexual relationships, risk behaviour, and Authors’ contributions condom use in the spread of sexually transmitted infections to heterosexual NY, KE and HN conceived of the study and built up the model. NY and men. Genitourin Med. 1997;73:368–72. KE conducted a systematic review. KE and NY drafted the first version of 16. 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Theoretical Biology and Medical ModellingSpringer Journals

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