Throughout the world, migrants are at greater risk for HIV than non-migrants [1–5]. Accordingly, if labour migration poses a significant risk for disease dissemination, the effect may be substantial in South Africa, the country with the greatest number of HIV cases in the world [6,7]. The South African population is highly mobile and includes millions of internal and foreign labour migrants. Such international mobility could, in turn, affect disease spread in neighbouring countries, where a considerable proportion of the adult population (up to 80% in Lesotho, for example) have lived as migrants in South Africa .
Although increased HIV rates among migrants would logically place their partners and their home communities at risk, this has not been established. The exact mechanisms leading to increased risk of HIV transmission among migrants, and potentially among their rural partners, have not been fully evaluated. Chief among the hypotheses explaining this increased risk are increased geographic connectedness and increased sexual risk behaviours. Migration increases contact between asynchronous epidemics, which would allow disease to flow from higher into lower prevalence areas. In the context of migration-associated social disruption, rates of change in partner can rise, leading to increased HIV exposure of migrants and subsequently their partners in the home community. The relative influence of each mechanisms is not known. Expanded information about these factors could direct targeted interventions for growing epidemics in mobile societies.
Other factors confound the role of migration by potentially minimizing the risks posed by migration in propagating the HIV epidemic. Some migrant workers do not have frequent contact with their partners, lowering the probability of HIV transmission between some couples. Additionally, the generalized growth of the epidemic in rural areas suggests that transmission within rural areas, rather than exclusive transmission between returning migrants and their partners, is now playing a greater role in the spread of HIV . Pinpointing the role of migration could have important implications for HIV control programs.
Early in the South African epidemic, migration appeared to fuel HIV spread by increasing geographic connectedness between locations with substantial differences in prevalence rates, such as migrant work sites and their rural home areas. In the mid-1990s, migrants in South Africa and Lesotho had levels of HIV infection close to seven times that of their non-migrant peers [10,11], and many early HIV cases were linked directly to migrant workers [12,13]. However, as the epidemic progressed and prevalence rose in rural areas, the distinction between areas of high and low prevalence has blurred, and rural epidemics may be self-sustaining .
Rural areas with relatively high HIV prevalence may continue to be influenced by migrants, not only because of migrants' connection to high-prevalence areas but also by migration-induced social disruption and increased high-risk sexual behaviour . Migrants may form more partnerships than they otherwise would have outside their home communities, while those who remain in rural communities, separated from their migrant partners, may also have higher partner change rates .
This study explores, through use of a mathematical model, the variable roles geography and sexual behaviour play in shaping the effect of migration on the rural HIV epidemic. The model uses data from a study of migrant and non-migrant men, and their rural partners, in northern KwaZulu/Natal, South Africa [5,9,15]. While previous HIV models have incorporated partnerships formed during migration , they have not formally evaluated the role of migration . The model in this paper addresses the cyclical pattern of migration, developed during the apartheid era in South Africa, in which migrants travel back and forth to work sites.
Other models of infectious disease transmission have employed a metapopulation approach, whereby disease transmission between isolated ‘patches’ (here, rural and urban communities) occurs via population movement. The resulting synchronized epidemics demonstrate both new fluctuations in disease incidence, as well as the persistence of diseases otherwise eradicated, as has been seen with measles, whooping cough, and severe acute respiratory syndrome [18–21]. Our model also employed metapopulation techniques to model disease dissemination between patches of asynchronous epidemics; however, in addition, it allowed for the evaluation of factors during distinct epidemic phases. This has proven increasingly important in understanding epidemic modifiers [22–25].
Background and data
The model developed here is based on biological and behavioural data collected in a cross-sectional study of migrant and non-migrant men and their rural partners in South Africa [5,9]. Like many parts of Southern Africa, Hlabisa, the rural area, is characterized by high rates of migration, with over 60% of adult men spending most nights away . Study participants were (a) migrant men from Hlabisa in one of two common migration destinations, Carletonville and Richards Bay; (b) their rural partners; and (c) rural couples in which neither partner was a migrant. Participants were tested for HIV and other sexually transmitted infections (STI), and were questioned about their health, sexual behaviour and migration history. This project was approved by the Ethics Committees of Johns Hopkins University School of Hygiene and Public Health and the University of KwaZulu-Natal, South Africa.
The two migration destinations were chosen because they reflected the prevalent patterns of migration. Carletonville is a gold mining town with a population of 300 000, of whom 80 000 are young men living on the mines. Working roughly 700 km from the rural area, migrants in Carletonville return home on average two or three times per year. By contrast, Richards Bay, an industrial town on the Kwazulu/Natal north coast, is much closer to Hlabisa, allowing migrants there to return home more frequently, often at the end of every month.
In the study, migrant men reported having more casual partners and being younger and better educated than non-migrant men. Migrant men were 2.4 times more likely to be HIV infected compared with non-migrant men (25.9% and 12.7%, respectively; P = 0.029) . HIV prevalence among rural migrants in Carletonville was 28.7% compared with 22.4% in Richards Bay. Migrant men in Carletonville – the distant destination – were 3.2 times more likely to be infected than their rural partners (28.7% and 11.1%, respectively), but migrants in Richards Bay were as likely to be infected as their rural partners (22.4% and 25.9%, respectively). Migrant couples were more than twice as likely to be HIV discordant compared with couples without a migrant partner (27% and 15%, respectively), and in one-third of discordant cases, it was the woman, not the migrating man, who was the infected partner . This last result challenges the common assumption about the unidirectionality of HIV spread in the context of migration.
A deterministic, compartmental model was designed to compare the effects of migration patterns and migration-associated risk behaviour. The model accounted for gender, HIV status and stage, heterogeneity in sexual behaviour, and partner choice. Additionally, the model accounted for infection by herpes simplex virus 2 (HSV-2) and a bacterial STI, both of which facilitate HIV transmission in this setting (see the Appendix; additional information about the mathematical model is available upon request from the corresponding author) [27–30]. The time between infection with an STI and treatment has not been adequately quantified, but in this community treatment is often delayed for a month or more [27,31,32]. Stage of HIV infection did not affect partner change rates in this model and age was not incorporated into the model.
The model depicted circular migration between Hlabisa and the two frequent migration destinations, Richards Bay and Carletonville. Men were divided into three non-overlapping groups: non-migrants, long-distance migrants and short-distance migrants. The model further allowed for the presence or absence of risk behaviour associated with migration. Such increased risk behaviour – or partner change – was derived from reported rates . For example, long-distance migrant men were more than four times as likely to have had a casual partner in the last year than non-migrant men (29.4% and 7.2%, respectively). Women almost uniformly reported only one regular and no casual partner in the Hlabisa study. Mixing between activity levels was based on previous work in other populations and assumptions regarding core groups [33–36]. Mixing between persons of different HIV states was assumed to be random.
Migration patterns were based on reported data from the Hlabisa study. Changes in migration frequency associated with the post-apartheid era were also recreated. A frequency of one return trip each year, the norm during apartheid, was compared with increasing migration rates to current levels. In addition, dissolution of steady, regular partnerships was assumed to occur approximately once a decade. The model assumed that migrants did not return simultaneously but staggered their trips throughout the year. These choices of parameters all led to a closer fit of the model to HIV prevalence data.
With data from the Hlabisa Migration Project, it was possible to generate prevalence rates close to those observed in Hlabisa in 2000, as shown in Fig. 1. Within Hlabisa, the actual overall prevalence rates in 2000 were closely matched by the modelled rates for 20 years into the epidemic . The observed prevalence of HIV among long-distance male migrants in 2000 was 28.7%, while the modelled prevalence was 29.9%. The observed prevalence of male short-distance migrants was 22.4% and the modelled prevalence was 22.2%. The result for non-migrants was lower than expected: 9.6% instead of the actual 12.6%.
The spread of HIV in these populations was modelled in the absence or presence of migration and migration-associated sexual risk behaviour. Results are shown for long-distance migrants, local women, and non-migrant men with parameters based on reported data (Fig. 2). The modelled epidemic spread more slowly in the absence of migration. Without migration and without increases in risk behaviour associated with migration, peak HIV prevalence rates were < 5% for all groups. Peak prevalence occurred later in the absence of migration-associated behaviour change, occurring by year 25 in populations with migration and behaviour change and by years 40–50 in the home populations in the absence of migration-associated behaviour change.
With migration added to the model, long-distance migrant men were at greatest risk as a result of their exposure to high HIV prevalence at the worksite (Fig. 2a). Their risk increased with migration alone (increasing from 5% to 12%), and was further compounded by migration-associated risk behaviour (up to a peak of 32.5% among long-distance migrants).
Among non-migrants, the epidemic initially grew more rapidly in the presence of migrants, but the migrants' increased risk did not elevate the long-term risk of their home communities if migration-associated risk behaviour was absent (Fig. 2b,c). In a mature epidemic without migration-associated risk behaviour, non-migrants had equal prevalence rates regardless of whether migrants were present in their community (Fig. 2b,c).
Long-term prevalence rates were elevated among non-migrant men and women only if migration was associated with increases in partner change rates, as observed in the data. Among long-distance migrants (Fig. 2a), the modelled HIV seroprevalence increased from 13% to 33% when known migration-associated sexual risk behaviour was included in the analysis. Likewise, among females in Hlabisa (Fig. 2b), long-term prevalence rates increased from 1.8% to 19% when migration-associated sexual risk behaviour among men was included. An increase from 3.7% to 6.4% was also seen among non-migrant men in Hlabisa in association with migration-associated sexual risk behaviour (Fig. 2c), despite a lack of change in either their own or their partners' sexual behaviours.
Frequency of migration affected HIV prevalence rates in the presence of migration-associated sexual behaviour change. If migration occurred infrequently and migration-associated sexual risk behaviour was assumed to be at current levels, the predicted epidemic would be one fifth that currently observed (2.8% compared with 15.1%; Fig. 3). Increasing migration frequency to current rates resulted in rapid epidemic growth to levels that would be equal to those which would have been seen if migration had always occurred at current rates.
Migration may impact HIV progression by linking geographically separate epidemics and by altering sexual behaviour. In our metapopulation model, increased geographic connectivity influenced HIV prevalence rates early in the epidemic, but this influence was outweighed by changes in sexual behaviour, which more strongly affected prevalence rates as the epidemic progressed.
The modelled rural epidemic grew substantially larger when high-risk behaviour among migrants was coupled with frequent return. In the past, South African couples separated by migration had little contact, and migrants would pass through the high-risk primary HIV phase and transient STI infections without transmitting the infection to their home partner. Since the early 1990s, however, migrants have been able to return home more frequently because of the ending of apartheid-era travel restrictions, increased flexibility of work contracts and the improvement of transportation between rural and urban areas. In the 1980s and before, migrants to Carletonville would return to their rural homes only at the end of the year . More frequent trips have helped to maintain high rate of STI and HIV because of continual contact between partners; yet this frequent contact failed to prevent the acquisition of casual partners while migrants are away.
The model also suggests that historical differences in migration patterns do not reduce long-term prevalence rates. As migrants return more frequently, incidence rapidly rises, overriding the protective effect of previous infrequent migration patterns. Hence, increases in home visits by migrants may have influenced the accelerated growth of the epidemic over the last 10 years. HIV prevention programmes need to address the increased risk behaviour seen among migrants, particularly frequent returners and short-term migrants, who have been shown to be at greater risk elsewhere in Africa [2,37,38].
Additional mechanisms of migration-influenced HIV transmission can be explored in future models. Women experience a rapid rise in HIV prevalence at younger ages, particularly in the long-distance migrant population studied here, with prevalence rates rising from 22.5% among sexually active 17–18 year olds to 64.7% among 22–24 year olds . Partnerships with significant age differences have been tied to increased transmission of HIV, with transmission from older men, where there is a high prevalence, to younger women . Migration may play a role in accelerating this effect, particularly given the high prevalence rates seen at the distant worksite. In addition, models could formally explore the parameterization of other mixing patterns – including factors such as sexual activity level and HIV status – as the model made assumptions based on other populations, though partner formation by high-risk individuals (such as those with primary HIV) may have an important impact [33–36].
Overall, the model indicates that if migration induces behaviour change then it will have a substantial influence on HIV prevalence. The role that migration has played in propagating the HIV epidemic has probably evolved over the course of the epidemic in South Africa. This model suggests that early in the epidemic, migration geographically linked discordant populations, thereby increasing HIV prevalence. However, in a more mature epidemic, such as that which South Africa currently faces, migration primarily increases HIV prevalence by increasing high-risk sexual behaviour. This high-risk behaviour can consequently affect the entire rural community. In this later stage of the epidemic, frequent return of migrants, without substantial reduction in risky sexual behaviour, only exacerbates the risk of HIV transmission. Programmes implemented solely to improve travel flexibility of migrants between their home community and worksite will not be sufficient to stem the effects of migration on the HIV epidemic. Measures need also to be taken to reduce the high-risk sexual behaviour associated with migration.
The authors would like to thank Brian Williams, Salim Abdool Karim, David Mkaya, A.W. Sturm, Joel Gittelsohn, Michael Sweat, Khongelani Zuma, Nozizwe Dladla and all other members of the Migration Project Team. Thanks also to Emily de Moor and Robert Shady for editorial assistance.
Sponsorship: The project was funded by the Wellcome Trust (grant 050517/z/97abc) and the South African Medical Research Council. The publication was made possible in part through support from an NIH training grant awarded to the Miriam Hospital (5T32 DA113911) and an NIH Career Development Award to Dr Lurie at Brown University (1K01 MH069113–01A1).
1. Poudel KC, Okumara J, Sherchand JB, Jimba M, Marakami I, Wakai S. Mumbai disease in far western Nepal: HIV infection and syphilis among male migrant-returnees and non-migrants. Trop Med Int Health 2003; 8:933–939.
2. Lagarde E, Schim van der Loeff M, Enel C, Holmgren B, Dray-Spira R, Pison G, et al
. Mobility and the spread of human immunodeficiency virus into rural areas of West Africa. Int J Epidemiol 2003; 32:753–754.
3. Wolffers I, Fernandez I. Migration
and AIDS. Lancet 1995; 346:1303.
4. Gras MJWJ, Langendam MW, Coutinho RA, van den Hoek A. HIV prevalence, sexual risk behaviour and sexual mixing patterns among migrants in Amsterdam, the Netherlands. AIDS 1999; 13:1953–1962.
5. Lurie MN, Williams BG, Zuma K, Mkaya-Mwamburi D, Garnett GP, Sturm AW, et al
. The impact of migration
on HIV-1 transmission in South Africa
:a study of migrant and nonmigrant men and their partners. Sex Transm Dis 2003; 30:149–156.
6. WHO UNAIDS. AIDS Epidemic Update
. Geneva: WHO/UNAIDS; 2005. Accessed: 28 February 2006 at http://www.unaids.org/epi/2005/doc/EPIupdate2005_pdf_en/epi-update2005_en.pdf
7. Department of Health, Republic of South Africa
. National HIV and Syphilis Antenatal Seroprevalence Survey in South Africa 2004
. Pretoria: South Africa
Department of Health; 2005. Accessed 28 February 2006 at http://www.doh.gov.za/docs/reports-f.html
8. McDonald DA. Toward a better understanding of cross-border migration
in Southern Africa. In: McDonald DA, editor. On borders: Perspectives on International Migration
in Southern Africa. New York: St Martin's Press; 2000. pp. 1–11.
9. Lurie MN, Williams BG, Zuma K, Mkaya-Mwamburi D, Garnett GP, Sweat MD, et al
. Who infects whom? HIV-1 concordance and discordance among migrant and non-migrant couples in South Africa
. AIDS 2003; 17:2235–2252.
10. Jochelson K, Mothibeli M, Leger JP. Human immunodeficiency virus and migrant labor in South Africa
. Int J Health Serv 1991; 21:157–173.
11. Kravitz JD MR, Petersen EA, Nyaphisis M, Human D. Human immunodeficiency virus seroprevalence in an occupational cohort in a South African community
. Arch Intern Med
12. Ramjee G, Abdool Karim SS, Sturm AW. Sexually transmitted infections among sex workers in KwaZulu/Natal, South Africa
. Sex Transm Dis 1998; 25:346–349.
13. Abdool Karim Q, Abdool Karim SS, Singh B, Short R, Ngxongo R. Seroprevalence of HIV infection in rural South Africa
. AIDS 1992; 6:1535–1539.
14. Decosas JKF, Anarfi JK, Sodji KD, Wagner HU. Migration
and AIDS. Lancet 1995; 346:826–828.
15. Lurie MN, Garnett G, Abdool Karim SS, Sturm A, Wilkinson D, Williams B. Migration and the Spread of HIV and other Sexually Transmitted Diseases in South Africa: Interlocking Urban and Rural Cohort Studies
. [study protocol] Providence, RI: Brown University Medical School; 1998. Accessed 2 November 2006 at http://www.brown.edu/Divisions/Medical_School/andera/profile.php?id=1100925759
16. Korenromp EL, van Vliet C, Grosskurth H, Gavyole A, van der Ploeg CPB, Fransen L, et al
. Model-based evaluation of single-round mass treatment of sexually transmitted diseases for HIV control in a rural African population. AIDS 2000; 14:573–593.
17. White RG. Commentary: what can we make of an association between human immunodeficiency virus prevalence and population mobility? Int J Epidemiol 2003; 32:753–754.
18. Bolker B, Grenfell B. Space, persistence and dynamics of measles epidemics. Philos Trans R Soc Lond B Biol Sci 1995; 348:309–320.
19. Finkenstadt B, Grenfell B. Empirical determinants of measles metapopulation dynamics in England and Wales. Proc R Soc Lond B Biol Sci 1998; 265:211–220.
20. Keeling MJ, Grenfell BT. Effect of variability in infection period on the persistence and spatial spread of infectious diseases. Math Biosci 1998; 147:207–226.
21. Broutin HF, Simondon F, Guegan JF. Whooping cough metapopulation dynamics in tropical conditions: disease persistence and impact of vaccination. Proc Biol Sci 2004; 271(Suppl 5):302–305.
22. Aral SO. Determinants of STD epidemics: implications for phase appropriate intervention strategies. Sex Transm Infect 2002; 78(Suppl 1):3–13.
23. Blanchard JF. Populations, pathogens, and epidemic phases: closing the gap between theory and practice in the prevention of sexually transmitted diseases. Sex Transm Infect 2002; 78(Suppl 1):183–188.
24. Low N. Phase specific strategies for the prevention, control, and elimination of sexually transmitted infections: case study in Lambeth, Southwark, and Lewisham, London, UK. Sex Transm Infect 2002; 78(Suppl 1):133–138.
25. Turner KM, Garnett GP. The impact of the phase of an epidemic of sexually transmitted infection on the evolution of the organism. Sex Transm Infect 2002; 78(Suppl 1):20–30.
26. Lurie MN, Harrison A, Wilkinson D, Abdool Karim SS. Circular migration
and sexual networking in rural KwaZulu/Natal: implications for the spread of HIV and other sexually transmitted diseases. Health Transit Rev 1997; 7(Suppl 3):17–27.
27. Wilkinson D, Wilkinson N. HIV infection among patients with sexually transmitted diseases in rural South Africa
. Int J STD AIDS 1998; 9:736–739.
28. Auvert B, Ballard R, Campbell C, Carael M, Carton M, Fehler G, et al
. HIV infection among youth in a South African mining town is associated with herpes simplex virus-2 seropositivity and sexual behaviour
. AIDS 2001; 15:885–898.
29. Chen CY, Ballard RC, Beck-Sague CM, Dangor Y, Radebe F, Schmid S, et al
. Human immunodeficiency virus infection and genital ulcer disease in South Africa
: the herpetic connection. Sex Transm Dis 2000; 27:21–29.
30. Garnett GP, Mertz KJ, Finelli L, Levine WC, St Louis ME. The transmission dynamics of gonorrhoea: modelling
the reported behaviour of infected patients from Newark, New Jersey. Philos Trans R Soc Lond B Biol Sci 1999; 354:787–797.
31. Harrison AD, Wilkinson, Lurie MN, Connolly AM, Abdool Karim SS. Improving quality of sexually transmitted disease case management in rural South Africa
32. Connolly AM, Wilkinson D, Harrison A, Lurie M, Abdool Karim SS. Inadequate treatment for sexually transmitted diseases in the South African private health sector. Int J STD AIDS 1999; 10:324–327.
33. Koopman J, Simon C, Jacquez J, Joseph J, Sattenspiel L, Park T. Sexual partner selectiveness effects on homosexual HIV transmission dynamics. J Acquir Immune Defic Syndr 1988; 1:486–504.
34. Anderson RM, Gupta S, Ng W. The significance of sexual partner contact networks for the transmission dynamics of HIV. J Acquir Immune Defic Syndr 1990; 3:417–429.
35. Garnett GP, Mertz KJ, Finelli L, Levne WC, St Louis ME. The transmission dynamics of gonorrhoea: modelling
the reported behaviour of infected patients from Newark, New Jersey. Philos Trans R Soc Lond B Biol Sci 1999; 354:787–797.
36. Renton A, Whitaker L, Ison C, Wadsworth J, Harris JR. Estimating the sexual mixing patterns in the general population from those in people acquiring gonorrhoea infection: theoretical foundation and empirical findings. J Epidemiol Community Health 1995; 49:205–213.
37. Pison G, Le Guenno B, Lagarde E, Enel C, Seck C. Seasonal migration
: a risk factor for HIV in rural Senegal. J Acquir Immune Defic Syndr 1993; 6:196–200.
38. Coffee M, Lurie MN, Garnett G. Modelling the impact of migration on the spread of HIV in South Africa
. XV International AIDS Conference
. Bangkok, July 2004 [abstract MoPeC3476].
39. Gregson S, Nyamukapa CA, Garnett GP, Mason PR, Zhuwau T, Carael M, et al
. Sexual mixing patterns and sex-differentials in teenage exposure to HIV infection in rural Zimbabwe. Lancet 2002; 359:1896–1903.
40. Paxton LA, Sewankambo N, Gray R, Serwadda D, McNairn D, Li C, et al
. Asymptomatic non-ulcerative genital tract infections in a rural Ugandan population. Sex Transm Infect 1998; 74:421–425.
41. Wilkinson D, Abdool Karim SS, Harrison A, Lurie MN, Colvin M, Connolly C, et al
. Unrecognised sexually transmitted infections in rural South African women: a hidden epidemic. Bull World Health Organ 1999; 77:22–28.
42. Morgan D, Maude GH, Malamba SS, Okongo MJ, Wagner HU, Mulder DW, et al
. HIV-1 disease progression and AIDS-defining disorders in rural Uganda. Lancet 1997; 350:245–250.
43. Sewankambo NK, Gray RH, Ahmad S, Serwadda D, Wabwire-Mangen F, Nalugoda F, et al
. Mortality associated with HIV infection in rural Rakai District, Uganda. AIDS 2000; 14:2391–2400.
44. Hooper RR, Reynolds GH, Jones DG, Zaidi A, Wiesner PJ, Latimer KP, et al
. Cohort study of venereal disease. 1: the risk of gonorrhea transmission from infected women to men. Am J Epidemiol 1978; 108:136–144.
45. Platt R, Rice PA, McCormack WM. Risk of acquiring gonorrhea and prevalence of abnormal adnexal findings among women recently exposed to gonorrhea. JAMA 1983; 250:3205–3209.
46. Koelle DM, Wald A. Herpes simplex virus: the importance of asymptomatic shedding. J Antimicrob Chemother 2000; 45(Suppl T3):1–8.
47. Casper C, Wald A. Condom use and the prevention of genital herpes acquisition. Herpes 2002; 9:10–14.
48. Wald A, Zeh J, Selke S, Warren T, Ashley R, Corey L. Genital shedding of herpes simplex virus among men. J Infect Dis 2002; 186(Suppl 1):34–39.
49. Gray RH, Wawer MJ, Brookmeyer R, Sewankambo NK, Swerwadda D, Wabwire-Mangen F, et al
. Probability of HIV-1 transmission per coital act in monogamous, heterosexual, HIV-1-discordant couples in Rakai, Uganda. Lancet 2001; 357:1149–1153.
50. Fleming DT, Wasserheit JN. From epidemiological synergy to public health policy and practice: the contribution of other sexually transmitted diseases to sexual transmission of HIV infection. Sex Transm Infect 1999; 75:3–17.
51. Rottingen JA, Cameron DW, Garnett GP. A systematic review of the epidemiologic interactions between classic sexually transmitted diseases and HIV: how much really is known? Sex Transm Dis 2001; 28:579–597.
The model population is stratified according to the following parameters: sex, subscript k; sexual activity level, subscript i; location and migration category, subscript q; infection status with bacterial STI, superscript s; viral STI, superscript v; stage of HIV infection, superscript h:
Changes in the variables are defined by ordinary differential equations determining the births and deaths and flows between infection states and geographic areas (available on request from the corresponding author). The force of infection for STI is given by
The force of infection for viral STI is given by
and for HIV is given by
Methods of determining patterns of mixing and the balance of sexual partnership between groups are also available on request. Staggered migration occurring en–masse annually and weekly:
The parameters values for modelling are given in Table A.
52. Korenromp EL, de Vlass SJ, Nagelkerke NJ, Habbema JD. Estimating the magnitude of STD cofactor effects on HIV transmission: how well can it be done? Sex Transm Dis 2001; 28:622–623.