Table of Contents Author Guidelines Submit a Manuscript
Interdisciplinary Perspectives on Infectious Diseases
Volume 2011, Article ID 267049, 10 pages
http://dx.doi.org/10.1155/2011/267049
Research Article

Pathogens, Social Networks, and the Paradox of Transmission Scaling

1Center for Infectious Disease Dynamics, Department of Biology, The Pennsylvania State University, University Park, PA 16802, USA
2Cardiff School of Biosciences, Cardiff University, Biomedical Sciences Building, Museum Avenue, Room C7.29, Cardiff CF10 3AX, UK
3Department of Veterinary Preventative Medicine, The Ohio State University, Columbus, OH 43210, USA
4Center for Infectious Disease Dynamics, Departments of Biology and Entomology, The Pennsylvania State University, University Park, PA 16802, USA

Received 24 September 2010; Revised 26 December 2010; Accepted 15 January 2011

Academic Editor: Katia Koelle

Copyright © 2011 Matthew J. Ferrari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Altizer, C. L. Nunn, P. H. Thrall et al., “Social organization and parasite risk in mammals: integrating theory and empirical studies,” Annual Review of Ecology, Evolution, and Systematics, vol. 34, pp. 517–547, 2003. View at Google Scholar · View at Scopus
  2. L. A. Meyers, B. Pourbohloul, M. E. J. Newman, D. M. Skowronski, and R. C. Brunham, “Network theory and SARS: predicting outbreak diversity,” Journal of Theoretical Biology, vol. 232, no. 1, pp. 71–81, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at MathSciNet · View at Scopus
  3. M. E. J. Newman, “Spread of epidemic disease on networks,” Physical Review E, vol. 66, no. 1, Article ID 016128, 11 pages, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Pastor-Satorras and A. Vespignani, “Epidemic spreading in scale-free networks,” Physical Review Letters, vol. 86, no. 14, pp. 3200–3203, 2001. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Bansal, B. T. Grenfell, and L. A. Meyers, “When individual behaviour matters: homogeneous and network models in epidemiology,” Journal of the Royal Society Interface, vol. 4, no. 16, pp. 879–891, 2007. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  6. R. M. Anderson and R. M. May, “Regulation and stability of host-parasite population interactions I. Regulatory processes,” Journal of Animal Ecology, vol. 47, pp. 219–247, 1978. View at Google Scholar
  7. M. C. M. de Jong, “Mathematical modelling in veterinary epidemiology: why model building is important,” Preventive Veterinary Medicine, vol. 25, no. 2, pp. 183–193, 1995. View at Google Scholar · View at Scopus
  8. G. Dwyer, J. S. Elkinton, and J. P. Buonaccorsi, “Host heterogeneity in susceptibility and disease dynamics: tests of a mathematical model,” American Naturalist, vol. 150, no. 6, pp. 685–707, 1997. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  9. H. McCallum, N. Barlow, and J. Hone, “How should pathogen transmission be modelled?” Trends in Ecology and Evolution, vol. 16, no. 6, pp. 295–300, 2001. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Begon, M. Bennett, R. G. Bowers, N. P. French, S. M. Hazel, and J. Turner, “A clarification of transmission terms in host-microparasite models: numbers, densities and areas,” Epidemiology and Infection, vol. 129, no. 1, pp. 147–153, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. M. J. Smith, S. Telfer, E. R. Kallio et al., “Host-pathogen time series data in wildlife support a transmission function between density and frequency dependence,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 19, pp. 7905–7909, 2009. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  12. P. H. Thrall, J. Antonovics, and D. W. Hall, “Host and pathogen coexistence in sexually transmitted and vector- borne diseases characterized by frequency-dependent disease transmission,” American Naturalist, vol. 142, no. 3, pp. 543–552, 1993. View at Publisher · View at Google Scholar · View at Scopus
  13. A. B. Lockhart, P. H. Thrall, and J. Antonovics, “Sexually transmitted diseases in animals: ecological and evolutionary implications,” Biological Reviews of the Cambridge Philosophical Society, vol. 71, no. 3, pp. 415–471, 1996. View at Google Scholar · View at Scopus
  14. F. De Castro and B. Bolker, “Mechanisms of disease-induced extinction,” Ecology Letters, vol. 8, no. 1, pp. 117–126, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. M. C. M. De Jong, O. Diekmann, and H. Heesterbeek, “How does transmission of infection depend on population size?” in Epidemic Models: Their Structure and Relation to Data, D. Mollison, Ed., pp. 84–94, Cambridge University Press, Cambridge, UK, 1995. View at Google Scholar
  16. W. M. Getz and J. Pickering, “Epidemic models: thresholds and population regulation,” The American Naturalist, vol. 121, pp. 892–898, 1983. View at Google Scholar
  17. R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, UK, 1991.
  18. J. Swinton, J. Harwood, B. T. Grenfell, and C. A. Gilligan, “Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations,” Journal of Animal Ecology, vol. 67, no. 1, pp. 54–68, 1998. View at Publisher · View at Google Scholar · View at Scopus
  19. O. N. Bjørnstad, B. F. Finkenstädt, and B. T. Grenfell, “Dynamics of measles epidemics: estimating scaling of transmission rates using a Time series SIR model,” Ecological Monographs, vol. 72, no. 2, pp. 169–184, 2002. View at Google Scholar · View at Scopus
  20. J. Swinton, J. Harwood, and A. Hall, “Scaling of phocine distemper virus transmission with harbor seal community size,” Ecologie, vol. 30, pp. 231–240, 1999. View at Google Scholar
  21. A. Bouma, M. C. M. de Jong, and T. G. Kimman, “Transmission of pseudorabies virus within pig populations is independent of the size of the population,” Preventive Veterinary Medicine, vol. 23, no. 3-4, pp. 163–172, 1995. View at Google Scholar · View at Scopus
  22. M. Begon, S. M. Feore, K. Bown, J. Chantrey, T. Jones, and M. Bennett, “Population and transmission dynamics of cowpox in bank voles: testing fundamental assumptions,” Ecology Letters, vol. 1, no. 2, pp. 82–86, 1998. View at Google Scholar · View at Scopus
  23. E. Bucheli and J. A. Shykoff, “The influence of plant spacing on density-dependent versus frequency-dependent spore transmission of the anther smut Microbotryum violaceum,” Oecologia, vol. 119, no. 1, pp. 55–62, 1999. View at Publisher · View at Google Scholar · View at Scopus
  24. P. Klepac, L. W. Pomeroy, O. N. Bjørnstad, T. Kuiken, A. D. M. E. Osterhaus, and J. M. Rijks, “Stage-structured transmission of phocine distemper virus in the Dutch 2002 outbreak,” Proceedings of the Royal Society B, vol. 276, no. 1666, pp. 2469–2476, 2009. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  25. R. J. Knell, M. Begon, and D. J. Thompson, “Transmission dynamics of Bacillus thuringiensis infecting Plodia interpunctella: a test of the mass action assumption with an insect pathogen,” Proceedings of the Royal Society of London B, vol. 263, no. 1366, pp. 75–81, 1996. View at Google Scholar
  26. R. J. Knell, M. Begon, and D. J. Thompson, “Transmission of Plodia interpunctella granulosis virus does not conform to the mass action model,” Journal of Animal Ecology, vol. 67, no. 4, pp. 592–599, 1998. View at Google Scholar · View at Scopus
  27. J. Antonovics and H. M. Alexander, “Epidemiology of Anther-Smut infection of Silene-alba (= S-Latifolia) caused by Ustilago-Violacea—patterns of spore deposition in experimental populations,” Proceedings of the Royal Society of London B, vol. 250, no. 1328, pp. 157–163, 1992. View at Google Scholar
  28. J. J. Ryder, K. M. Webberley, M. Boots, and R. J. Knell, “Measuring the transmission dynamics of a sexually transmitted disease,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 42, pp. 15140–15143, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  29. W. J. Edmunds, G. F. Medley, D. J. Nokes, C. J. O'Callaghan, H. C. Whittle, and A. J. Hall, “Epidemiological patterns of hepatitis B virus (HBV) in highly endemic areas,” Epidemiology and Infection, vol. 117, no. 2, pp. 313–325, 1996. View at Google Scholar · View at Scopus
  30. J. R. Torres and A. Mondolfi, “Protracted outbreak of severe delta hepatitis: experience in an isolated Amerindian population of the Upper Orinoco Basin,” Reviews of Infectious Diseases, vol. 13, no. 1, pp. 52–55, 1991. View at Google Scholar · View at Scopus
  31. M. Hu, D. Schenzle, F. Deinhardt, and R. Scheid, “Prevalence of markers of hepatitis A and B in the Shanghai area,” Journal of Infectious Diseases, vol. 147, no. 2, p. 360, 1983. View at Google Scholar · View at Scopus
  32. C. J. E. Metcalf et al., “The epidemiology of rubella in Mexico: seasonality, stochasticity and regional variation,” Epidemiology and Infection. In press. View at Publisher · View at Google Scholar · View at PubMed
  33. L. J. Rachowicz and C. J. Briggs, “Quantifying the disease transmission function: effects of density on Batrachochytrium dendrobatidis transmission in the mountain yellow-legged frog Rana muscosa,” Journal of Animal Ecology, vol. 76, no. 4, pp. 711–721, 2007. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  34. H. McCallum, M. Jones, C. Hawkins et al., “Transmission dynamics of Tasmanian devil facial tumor disease may lead to disease-induced extinction,” Ecology, vol. 90, no. 12, pp. 3379–3392, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. R. M. Anderson, H. C. Jackson, R. M. May, and A. M. Smith, “Population dynamics of fox rabies in Europe,” Nature, vol. 289, no. 5800, pp. 765–771, 1981. View at Google Scholar · View at Scopus
  36. R. N. Basu, Z. Jezek, and N. A. Ward, The Eradication of Smallpox in India, World Health Organization, Geneva, Switzerland, 1979.
  37. M. J. Keeling, M. E. J. Woolhouse, R. M. May, G. Davies, and B. T. Grenfell, “Modelling vaccination strategies against foot-and-mouth disease,” Nature, vol. 421, no. 6919, pp. 136–142, 2003. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  38. C. J. Rhodes and R. M. Anderson, “Epidemic thresholds and vaccination in a lattice model of disease spread,” Theoretical Population Biology, vol. 52, no. 2, pp. 101–118, 1997. View at Publisher · View at Google Scholar · View at PubMed
  39. J. Turner, M. Begon, and R. G. Bowers, “Modelling pathogen transmission: the interrelationship between local and global approaches,” Proceedings of the Royal Society B, vol. 270, no. 1510, pp. 105–112, 2003. View at Publisher · View at Google Scholar · View at PubMed
  40. M. Boots, P. J. Hudson, and A. Sasaki, “Large shifts in pathogen virulence relate to host population structure,” Science, vol. 303, no. 5659, pp. 842–844, 2004. View at Publisher · View at Google Scholar · View at PubMed
  41. S. N. Wood and M. B. Thomas, “Space, time and persistence of virulent pathogens,” Proceedings of the Royal Society B, vol. 263, no. 1371, pp. 673–680, 1996. View at Publisher · View at Google Scholar · View at PubMed
  42. J. M. Read and M. J. Keeling, “Disease evolution on networks: the role of contact structure,” Proceedings of the Royal Society B, vol. 270, no. 1516, pp. 699–708, 2003. View at Publisher · View at Google Scholar · View at PubMed
  43. J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp, and W. M. Getz, “Superspreading and the effect of individual variation on disease emergence,” Nature, vol. 438, no. 7066, pp. 355–359, 2005. View at Publisher · View at Google Scholar · View at PubMed
  44. M. E. J. Woolhouse, C. Dye, J. F. Etard et al., “Heterogeneities in the transmission of infectious agents: implications for the design of control programs,” Proceedings of the National Academy of Sciences of the United States of America, vol. 94, no. 1, pp. 338–342, 1997. View at Publisher · View at Google Scholar
  45. W. Jetz, C. Carbone, J. Fulford, and J. H. Brown, “The scaling of animal space use,” Science, vol. 306, no. 5694, pp. 266–268, 2004. View at Publisher · View at Google Scholar · View at PubMed
  46. M. Sjöberg, B. Albrectsen, and J. Hjältén, “Truncated power laws: a tool for understanding aggregation patterns in animals?” Ecology Letters, vol. 3, no. 2, pp. 90–94, 2000. View at Publisher · View at Google Scholar
  47. S. E. Perkins, F. Cagnacci, A. Stradiotto, D. Arnoldi, and P. J. Hudson, “Comparison of social networks derived from ecological data: implications for inferring infectious disease dynamics,” Journal of Animal Ecology, vol. 78, no. 5, pp. 1015–1022, 2009. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  48. C. Song, Z. Qu, N. Blumm, and A. L. Barabási, “Limits of predictability in human mobility,” Science, vol. 327, no. 5968, pp. 1018–1021, 2010. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  49. M. Molloy and B. Reed, “A critical-point for random graphs with a given degree sequence,” Random Structures & Algorithms, vol. 6, no. 2-3, pp. 161–179, 1995. View at Google Scholar
  50. R. Pastor-Satorras and A. Vespignani, “Epidemic dynamics in finite size scale-free networks,” Physical Review E, vol. 65, no. 3, Article ID 035108, 4 pages, 2002. View at Publisher · View at Google Scholar
  51. N. T. J. Bailey, The Mathematical Theory of Epidemics, Griffin, London, UK, 1957.
  52. M. J. Ferrari, S. Bansal, L. A. Meyers, and O. N. Bjørnstad, “Network frailty and the geometry of herd immunity,” Proceedings of the Royal Society B, vol. 273, no. 1602, pp. 2743–2748, 2006. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  53. A. L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  54. S. Bansal et al., “The dynamic nature of contact networks in infectious disease epidemiology,” Journal of Biological Dynamics, vol. 4, no. 5, pp. 478–489, 2010. View at Google Scholar
  55. J. Saramäki and K. Kaski, “Modelling development of epidemics with dynamic small-world networks,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 413–421, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at MathSciNet · View at Scopus
  56. M. S. Handcock and J. H. Jones, “Likelihood-based inference for stochastic models of sexual network formation,” Theoretical Population Biology, vol. 65, no. 4, pp. 413–422, 2004. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  57. M. C. González, C. A. Hidalgo, and A. L. Barabási, “Understanding individual human mobility patterns,” Nature, vol. 453, no. 7196, pp. 779–782, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  58. N. Becker and J. Angulo, “On estimating the contagiousness of a disease transmitted from person to person,” Mathematical Biosciences, vol. 54, no. 1-2, pp. 137–154, 1981. View at Publisher · View at Google Scholar · View at Scopus
  59. S. Altizer, W. M. Hochachka, and A. A. Dhondt, “Seasonal dynamics of mycoplasmal conjunctivitis in eastern North American house finches,” Journal of Animal Ecology, vol. 73, no. 2, pp. 309–322, 2004. View at Publisher · View at Google Scholar · View at Scopus
  60. P. Caley and D. Ramsey, “Estimating disease transmission in wildlife, with emphasis on leptospirosis and bovine tuberculosis in possums, and effects of fertility control,” Journal of Applied Ecology, vol. 38, no. 6, pp. 1362–1370, 2001. View at Publisher · View at Google Scholar · View at Scopus
  61. P. C. Cross, D. M. Heisey, B. M. Scurlock, W. H. Edwards, M. R. Ebinger, and A. Brennan, “Mapping brucellosis increases relative to elk density using hierarchical bayesian models,” PLoS One, vol. 5, no. 4, 2010. View at Publisher · View at Google Scholar · View at PubMed
  62. N. D. Barlow, “Non-linear transmission and simple models for bovine tuberculosis,” Journal of Animal Ecology, vol. 69, no. 4, pp. 703–713, 2000. View at Publisher · View at Google Scholar · View at Scopus
  63. A. L. Greer, C. J. Briggs, and J. P. Collins, “Testing a key assumption of host-pathogen theory: density and disease transmission,” Oikos, vol. 117, no. 11, pp. 1667–1673, 2008. View at Publisher · View at Google Scholar · View at Scopus
  64. R. Woodroffe, C. A. Donnelly, G. Wei et al., “Social group size affects Mycobacterium bovis infection in European badgers (Meles meles),” Journal of Animal Ecology, vol. 78, no. 4, pp. 818–827, 2009. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus