A statistical network analysis of the HIV/AIDS epidemics in Cuba

  • Stéphan Clémençon
  • Hector De Arazoza
  • Fabrice Rossi
  • Viet Chi Tran
Original Article


The Cuban contact-tracing detection system set up in 1986 allowed the reconstruction and analysis of the sexual network underlying the epidemic (5389 vertices and 4073 edges, giant component of 2386 nodes and 3168 edges), shedding light onto the spread of HIV and the role of contact-tracing. Clustering based on modularity optimization provides a better visualization and understanding of the network, in combination with the study of covariates. The graph has a globally low but heterogeneous density, with clusters of high intraconnectivity but low interconnectivity. Though descriptive, our results pave the way for incorporating structure when studying stochastic SIR epidemics spreading on social networks.


Cuban HIV/AIDS epidemics Contact-tracing Social network Graph-mining Clustering 



This work has been funded by ANR Viroscopy (ANR-08-SYSC-016-03), Chaire Mathématiques et Modélisation de la Biodiversité (Ec. Polytechnique, Museum National d’Histoire Naturelle et Fondation X), ANR MANEGE (ANR-09-BLAN-0215) and Labex CEMPI (ANR-11-LABX-0007-01). H. De Arazoza received support from the Spanish project AECID A2/038418/11. The authors thank Dr. J. Perez of the National Institute of Tropical Diseases in Cuba for granting access to the HIV/AIDS database. They also thank Ms. D. Abu Awad for reviewing the English language.

Supplementary material

13278_2015_291_MOESM1_ESM.pdf (1.7 mb)
Supplementary material 1 (pdf 1717 KB)
13278_2015_291_MOESM2_ESM.mp4 (3.6 mb)
An mp4 film showing how the giant component is built with time is also provided in the electronic supplementary material. Supplementary material 2(MP4 3659 kb)


  1. Ahuja R, Magnanti T, Orlin J (1993) Network flows: theory, algorithms and applications. Prentice Hall, New JerseyzbMATHGoogle Scholar
  2. Auvert B, de Arazoza H, Clémençon S, Perez J, Lounes R (2007) The HIV/AIDS epidemic in Cuba: description and tentative explanation of its low hiv prevalence. BMC Infect Dis 7(30)Google Scholar
  3. Ball F, Neal P (2008) Network epidemic models with two levels of mixing. Math Biosci 212:69–87MathSciNetCrossRefzbMATHGoogle Scholar
  4. Ball F, Sirl D, Trapman P (2014) Epidemics on random intersection graphs. Ann Appl Probab 24(3):1081–1128MathSciNetCrossRefzbMATHGoogle Scholar
  5. Barbour AD, Reinert G (2013) Approximating the epidemic curve. Electron J Probab 18(54):1–30MathSciNetGoogle Scholar
  6. Blum M, Tran VC (2010) HIV with contact-tracing: a case study in approximate Bayesian computation. Biostatistics 11(4):644–660CrossRefGoogle Scholar
  7. Britton T, Deijfen M, Lagerås A, Lindholm M (2008) Epidemics on random graphs with tunable clustering. J Appl Probab 45:743–756MathSciNetCrossRefzbMATHGoogle Scholar
  8. Chan SK, Thornton LR, Chronister KJ, Meyer J, Wolverton M, Johnson CK, Arafat RR, Joyce P, Switzer WM, Heneine W, Shankar A, Granade T, Michele Owen S, Sprinkle P, Sullivan V (2014) Likely female-to-female sexual transmission of HIV —Texas. MMWR Morb Mortal Wkly Rep 63(10):209–212Google Scholar
  9. Clauset A, Shalizi C, Newman M (2009) Power-law distributions in empirical data. SIAM Rev 51:661–703MathSciNetCrossRefzbMATHGoogle Scholar
  10. Clémençon S, De Arazoza H, Rossi F, Tran VC (2011a) Hierarchical clustering for graph visualization. In: Proceedings of XVIIIth European symposium on artificial neural networks (ESANN 2011), Bruges, pp 227–232Google Scholar
  11. Clémençon S, De Arazoza H, Rossi F, Tran VC (2011) Visual mining of epidemic networks. In: Cabestany J, Rojas I, Joya G (eds) Advances in computational intelligence. Proceedings of 11th international work-conference on artificial neural networks (IWANN 2011), Lecture Notes in Computer Science, vol 6692. Springer, Berlin, pp 276–283Google Scholar
  12. Clémençon S, De Arazoza H, Rossi F, Tran VC (2015) Supplementary materials for “A network analysis of the HIV-AIDS epidemics in Cuba”Google Scholar
  13. Clémençon S, Tran VC, De Arazoza H (2008) A stochastic SIR model with contact-tracing: large population limits and statistical inference. J Biol Dyn 2(4):391–414CrossRefGoogle Scholar
  14. De Arazoza H, Lounes R (2002) A nonlinear model for sexually transmitted disease with contact-tracing. J Math Appl Med Biol 19:221–234CrossRefzbMATHGoogle Scholar
  15. Decreusefond L, Dhersin J-S, Moyal P, Tran VC (2011) Large graph limit for a sir process in random network with heterogeneous connectivity. Ann Appl Probab 22(2):541–575MathSciNetCrossRefGoogle Scholar
  16. Di Battista G, Eades P, Tamassia R, Tollis IG (1999) Graph drawing: algorithms for the visualization of graphs. Prentice Hall, New JerseyGoogle Scholar
  17. Durrett R (2006) Random graph dynamics. Cambridge University Press, CambridgeGoogle Scholar
  18. Fortunato S, Barthélemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci 104(1):36–41CrossRefGoogle Scholar
  19. Fruchterman T, Reingold B (1991) Graph drawing by force-directed placement. Softw Pract Exp 21:1129–1164CrossRefGoogle Scholar
  20. Graham M, House T (2013) Dynamics of stochastic epidemics on heterogeneous networks. J Math Biol 68:1583–1605MathSciNetCrossRefGoogle Scholar
  21. Herman I, Melançon G, Scott Marshall M (2000) Graph visualization and navigation in information visualisation. IEEE Trans Vis Comput Graphics 6(1):24–43CrossRefGoogle Scholar
  22. Hill B (1975) A simple general approach to inference about the tail of a distribution. Ann Stat 3(5):1163–1174CrossRefzbMATHGoogle Scholar
  23. House T (2012) Modelling epidemics on networks. Contemp Phys 53(3):213–225CrossRefGoogle Scholar
  24. Hsieh Y-H, Wang Y-S, Arazoza HD, Lounes R (2010) Modeling secondary level of HIV contact tracing: its impact on HIV intervention in Cuba. BMC Infect Dis 10:194CrossRefGoogle Scholar
  25. Kiss I, Green D, Kao R (2013) Infectious disease control using contact tracing in random and scale-free networks. J R Soc Interface 3(6):55–62CrossRefGoogle Scholar
  26. Kleczkowski A, Grenfell B (1999) Mean-field-type equations for spread of epidemics: the small world model. Phys A 274:355–360CrossRefGoogle Scholar
  27. May RM, Lloyd AL (2001) Infection dynamics on scale-free networks. Phys Rev E 64:066112CrossRefGoogle Scholar
  28. Molloy M, Reed B (1995) A critical point for random graphs with a given degree sequence. Random Struct Algorithms 6(2/3):161–179MathSciNetCrossRefzbMATHGoogle Scholar
  29. Moore C, Newman M (2000) Epidemics and percolation in small-world networks. Phys Rev E 61:5678–5682CrossRefGoogle Scholar
  30. Newman M (2003) Mixing patterns in networks. Phys Rev E 67:026126MathSciNetCrossRefGoogle Scholar
  31. Newman M (2003) The structure and function of complex networks. SIAM Rev 45:167–256MathSciNetCrossRefzbMATHGoogle Scholar
  32. Newman M, Barabási A, Watts D (2006) The structure and dynamics of networks. Princeton University Press, PrincetonzbMATHGoogle Scholar
  33. Newman M, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113CrossRefGoogle Scholar
  34. Newman M, Strogatz S, Watts D (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E 64(2):026118CrossRefGoogle Scholar
  35. Noack A (2009) Modularity clustering is force-directed layout. Phys Rev E 79(026102)Google Scholar
  36. Noack A, Rotta R (2009) Multi-level algorithms for modularity clustering. In: SEA ’09: Proceedings of the 8th international symposium on experimental algorithms. Springer, Berlin, pp 257–268Google Scholar
  37. Pastor-Satorras R, Vespignani A (2002) Epidemics and immunization in scale-free networks. In: Handbook of graphs and networks: from the genome to the internet. Wiley-VCH, Berlin, pp 113–132Google Scholar
  38. Reichardt J, Bornholdt S (2007) Partitioning and modularity of graphs with arbitrary degree distribution. Phys Rev E 76(1):015102MathSciNetCrossRefGoogle Scholar
  39. Resnick S (2007) Heavy-tail phenomena. Springer, BerlinzbMATHGoogle Scholar
  40. Roberts JM Jr (2000) Simple methods for simulating sociomatrices with given marginal totals. Soc Netw 22(3):273–283CrossRefGoogle Scholar
  41. Rossi F, Villa-Vialaneix N (2011) Représentation d’un grand réseau à partir d’une classification hiérarchique de ses sommets. Journal de la Société Française de Statistique 152(3):34–65MathSciNetGoogle Scholar
  42. Rothenberg R, Woodhouse D, Potterat J, Muth S, Darrow W, Klovdahl A (1995) Social networks in disease transmission: the Colorado Springs study. In: Needle R, Coyle S, Genser S, Trotter II, RT (eds) Social networks, drug abuse and HIV transmission, Research Monographs, vol 151. National Institute, pp 3–18Google Scholar
  43. Tunkelang D (1999) A numerical optimization approach to general graph drawing. PhD thesis, School of Computer Science, Carnegie Mellon University, CMU-CS-98-189Google Scholar
  44. Volz E (2008) SIR dynamics in random networks with heterogeneous connectivity. J Math Biol 56:293–310MathSciNetCrossRefzbMATHGoogle Scholar
  45. Volz E, Meyers LA (2007) Susceptible-infected-recovered epidemics in dynamic contact networks. Proc R Soc B 274:2925–2933CrossRefGoogle Scholar
  46. Wylie J, Jolly A (2001) Patterns of Chlamydia and Gonorrhea infection in sexual networks in Manitoba, Canada. Sex Transm Dis 28(1):14–24CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Institut Telecom, LTCI UMR Telecom ParisTech/CNRS 5141ParisFrance
  2. 2.Université René Descartes, MAP5 UMR CNRS 8145ParisFrance
  3. 3.Facultad de Matemática y ComputaciónUniversidad de la HabanaLa HabanaCuba
  4. 4.SAMM EA 4543Université Paris 1 Panthé on-Sorbonne, Centre PMFParis Cedex 13France
  5. 5.Laboratoire Paul PainlevéUMR CNRS 8524, Université Lille 1Villeneuve d’Ascq CedexFrance

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