2014, 11(5): 1065-1090. doi: 10.3934/mbe.2014.11.1065

What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics?

1. 

Department of Global Health, University of Washington. Box 359927, 325 Ninth Ave Seattle WA 98104, United States

2. 

Fred Hutchinson Cancer Research Center, PO Box 19024, 1100 Fairview Ave. N. Seattle WA 98109, United States

3. 

Department of Anthropology, University of Washington, Campus Box 353100, Seattle WA 98195, United States

Received  December 2013 Revised  February 2014 Published  June 2014

Circular migrations are the periodic movement of individuals between multiple locations, observed in parts of sub-Saharan Africa. Relationships between circular migrations and HIV are complex, entailing interactions between migration frequency, partnership structure, and exposure to acute HIV infection. Mathematical modeling is a useful tool for understanding these interactions.
    Two modeling classes have dominated the HIV epidemiology and policy literature for the last decade: one a form of compartmental models, the other network models. We construct models from each class, using ordinary differential equations and exponential random graph models, respectively.
    Our analysis suggests that projected HIV prevalence is highly sensitive to the choice of modeling framework. Assuming initial equal HIV prevalence across locations, compartmental models show no association between migration frequency and HIV prevalence or incidence, while network models show that migrations at frequencies shorter than the acute HIV period predict greater HIV incidence and prevalence compared to longer migration periods. These differences are statistically significant when network models are extended to incorporate a requirement for migrant men's multiple partnerships to occur in different locations. In settings with circular migrations, commonly-used forms of compartmental models appear to miss key components of HIV epidemiology stemming from interactions of relational and viral dynamics.
Citation: Aditya S. Khanna, Dobromir T. Dimitrov, Steven M. Goodreau. What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics?. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1065-1090. doi: 10.3934/mbe.2014.11.1065
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show all references

References:
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M. C. Boily, D. Dimitrov, S. S. Abdool Karim and B. Masse, The future role of rectal and vaginal microbicides to prevent HIV infection in heterosexual populations: Implications for product development and prevention,, Sex. Transm. Infect., 87 (2011), 646. doi: 10.1136/sextrans-2011-050184.

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N. B. Carnegie and M. Morris, Size matters: Concurrency and the epidemic potential of HIV in small networks,, PLoS ONE, 7 (2012). doi: 10.1371/journal.pone.0043048.

[10]

S. Cassels, Samuel J. Clark and M. Morris, Mathematical models for HIV transmission dynamics,, JAIDS- Journal of Acquired Immune Deficiency Syndrome, 47 (2008). doi: 10.1097/QAI.0b013e3181605da3.

[11]

E. Coast, Local understandings of, and responses to, HIV: Rural-urban migrants in Tanzania,, Social Science & Medicine, 63 (2006), 1000. doi: 10.1016/j.socscimed.2006.03.009.

[12]

M. P. Coffee, G. P. Garnett, M. Mlilo, H. A. C. M. Voeten, S. Chandiwana and S. Gregson, Patterns of movement and risk of HIV infection in rural Zimbabwe,, Journal of Infectious Diseases, 191 (2005). doi: 10.1086/425270.

[13]

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[14]

D. F. Cuadros, P. H. Crowley, B. Augustine, S. L. Stewart and G. Garcia-Ramos, Effect of variable transmission rate on the dynamics of HIV in sub-Saharan Africa,, BMC Infect. Dis., 11 (2011). doi: 10.1186/1471-2334-11-216.

[15]

K. D. Deane, J. O. Parkhurst and D. Johnston, Linking migration, mobility and HIV,, Tropical Medicine & International Health, 15 (2010), 1458. doi: 10.1111/j.1365-3156.2010.02647.x.

[16]

K. Dietz and K. P. Hadeler, Epidemiological models for sexually transmitted diseases,, J. Math. Biol., 26 (1988), 1. doi: 10.1007/BF00280169.

[17]

K. Dietz and W. Tudor, Triangles in heterosexual HIV transmission,, in AIDS Epidemiology: Methodological Issues (eds. N. P. Jewell, (1992), 143. doi: 10.1007/978-1-4757-1229-2_7.

[18]

D. T. Dimitrov, M. C. Boily, R. F. Baggaley and B. Masse, Modeling the gender-specific impact of vaginal microbicides on HIV transmission,, J. Theor. Biol., 288 (2011), 9. doi: 10.1016/j.jtbi.2011.08.001.

[19]

J. W. Eaton, L. F. Johnson, J. A. Salomon, T. Barnighausen, E. Bendavid, A. Bershteyn, D. E. Bloom, V. Cambiano, C. Fraser, J. A. Hontelez, S. Humair, D. J. Klein, E. F. Long, A. N. Phillips, C. Pretorius, J. Stover, E. A. Wenger, B. G. Williams and T. B. Hallett, HIV Treatment as Prevention: Systematic Comparison of Mathematical Models of the Potential Impact of Antiretroviral Therapy on HIV Incidence in South Africa,, PLoS Medicine, 9 (2012). doi: 10.1371/journal.pmed.1001245.

[20]

E. A. Enns, M. L. Brandeau, T. K. Igeme and E. Bendavid, Assessing effectiveness and cost-effectiveness of concurrency reduction for HIV prevention,, Int. J. STD AIDS, 22 (2011), 558. doi: 10.1258/ijsa.2011.010322.

[21]

G. P. Garnett, P. J. White and H. Ward, Fewer partners or more condoms? Modelling the effectiveness of STI prevention interventions,, Sex. Transm. Infect., 84 (2008), 4. doi: 10.1136/sti.2008.029850.

[22]

G. B. Gomez, A. Borquez, C. F. Caceres, E. R. Segura, R. M. Grant, G. P. Garnett and T. B. Hallett, The potential impact of pre-exposure prophylaxis for HIV prevention among men who have sex with men and transwomen in Lima, Peru: A mathematical modelling study,, PLoS Med., 9 (2012). doi: 10.1371/journal.pmed.1001323.

[23]

S. M. Goodreau, L. P. Goicochea and J. Sanchez, Sexual role and transmission of HIV Type 1 among men who have sex with men, in Peru,, J. Infect. Dis., 191 (2005). doi: 10.1086/425268.

[24]

S. M. Goodreau and M. R. Golden, Biological and demographic causes of high HIV and sexually transmitted disease prevalence in men who have sex with men,, Sex. Transm. Infect., 83 (2007), 458. doi: 10.1136/sti.2007.025627.

[25]

S. M. Goodreau, S. Cassels, D. Kasprzyk, D. E. Montao, A. Greek and M. Morris, Concurrent partnerships, acute infection and HIV epidemic dynamics among young adults in Zimbabwe,, AIDS and Behavior, 16 (2012), 312. doi: 10.1007/s10461-010-9858-x.

[26]

S. M. Goodreau, A decade of modelling research yields considerable evidence for the importance of concurrency: A response to Sawers and Stillwaggon,, Journal of the International AIDS Society, 14 (2011). doi: 10.1186/1758-2652-14-12.

[27]

S. M. Goodreau, N. B. Carnegie, E. Vittinghoff, J. R. Lama, J. Sanchez, B. Grinsztejn, B. A. Koblin, K. H. Mayer and S. P. Buchbinder, What drives the US and Peruvian HIV epidemics in men who have sex with men (MSM)?, PLoS ONE, 7 (2012). doi: 10.1371/journal.pone.0050522.

[28]

K. P. Hadeler, R. Waldstatter and A. Worz-Busekros, Models for pair formation in bisexual populations,, J. Math. Biol., 26 (1988), 635. doi: 10.1007/BF00276145.

[29]

M. S. Handcock, D. R. Hunter, C. T. Butts, S. M. Goodreau and M. Morris, Statnet: Software Tools for the Statistical Modeling of Network Data,, Seattle, (2003).

[30]

T. D. Hollingsworth, R. M. Anderson and C. Fraser, HIV-1 transmission, by stage of infection,, Journal Of Infectious Diseases, 198 (2008), 687. doi: 10.1086/590501.

[31]

D. R. Hunter, S. M. Goodreau and M. S. Handcock, Goodness of fit of social network models,, Journal of the American Statistical Association, 103 (2008), 248. doi: 10.1198/016214507000000446.

[32]

L. F. Johnson and P. J. White, A review of mathematical models of HIV/AIDS interventions and their implications for policy,, Sex. Transm. Infect., 87 (2011), 629. doi: 10.1136/sti.2010.045500.

[33]

M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals,, Princeton University Press, (2008).

[34]

M.J. Keeling and P. Rohani, Estimating spatial coupling in epidemiological systems: A mechanistic approach,, Ecology Letters, 5 (2002), 20. doi: 10.1046/j.1461-0248.2002.00268.x.

[35]

J. H. Kim and J. S. Koopman, HIV transmissions by stage in dynamic sexual partnerships,, J. Theor. Biol., 298 (2012), 147. doi: 10.1016/j.jtbi.2011.12.021.

[36]

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