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Proceedings of the Royal Society B: Biological Sciences logoLink to Proceedings of the Royal Society B: Biological Sciences
. 2004 Aug 7;271(Suppl 5):S364–S366. doi: 10.1098/rsbl.2004.0188

Polynomial epidemics and clustering in contact networks.

Balázs Szendroi 1, Gábor Csányi 1
PMCID: PMC1810049  PMID: 15504019

Abstract

It is widely known that the spread of the human immunodeficiency virus was slower than exponential in several populations, even at the very beginning of the epidemic. We show that this implies a significant reduction in the effective reproductive rate of the epidemic, and describe a general mechanism, related to the clustering properties of the disease transmission network, that is capable of explaining this reduction. Our considerations provide what is, to our knowledge, a new angle on polynomial epidemic processes, and may have implications for the choice of strategy against such epidemics.

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Selected References

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  1. Barabasi AL, Albert R. Emergence of scaling in random networks. Science. 1999 Oct 15;286(5439):509–512. doi: 10.1126/science.286.5439.509. [DOI] [PubMed] [Google Scholar]
  2. Colgate S. A., Stanley E. A., Hyman J. M., Layne S. P., Qualls C. Risk behavior-based model of the cubic growth of acquired immunodeficiency syndrome in the United States. Proc Natl Acad Sci U S A. 1989 Jun;86(12):4793–4797. doi: 10.1073/pnas.86.12.4793. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Keeling M. J., Rand D. A., Morris A. J. Correlation models for childhood epidemics. Proc Biol Sci. 1997 Aug 22;264(1385):1149–1156. doi: 10.1098/rspb.1997.0159. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Klovdahl A. S. Social networks and the spread of infectious diseases: the AIDS example. Soc Sci Med. 1985;21(11):1203–1216. doi: 10.1016/0277-9536(85)90269-2. [DOI] [PubMed] [Google Scholar]
  5. Lloyd A. L., May R. M. Epidemiology. How viruses spread among computers and people. Science. 2001 May 18;292(5520):1316–1317. doi: 10.1126/science.1061076. [DOI] [PubMed] [Google Scholar]
  6. May R. M., Anderson R. M. The transmission dynamics of human immunodeficiency virus (HIV). Philos Trans R Soc Lond B Biol Sci. 1988 Oct 31;321(1207):565–607. doi: 10.1098/rstb.1988.0108. [DOI] [PubMed] [Google Scholar]
  7. May R. M., Anderson R. M. Transmission dynamics of HIV infection. Nature. 1987 Mar 12;326(6109):137–142. doi: 10.1038/326137a0. [DOI] [PubMed] [Google Scholar]
  8. Pastor-Satorras R., Vespignani A. Epidemic spreading in scale-free networks. Phys Rev Lett. 2001 Apr 2;86(14):3200–3203. doi: 10.1103/PhysRevLett.86.3200. [DOI] [PubMed] [Google Scholar]
  9. Potterat J. J., Zimmerman-Rogers H., Muth S. Q., Rothenberg R. B., Green D. L., Taylor J. E., Bonney M. S., White H. A. Chlamydia transmission: concurrency, reproduction number, and the epidemic trajectory. Am J Epidemiol. 1999 Dec 15;150(12):1331–1339. doi: 10.1093/oxfordjournals.aje.a009965. [DOI] [PubMed] [Google Scholar]
  10. Read Jonathan M., Keeling Matt J. Disease evolution on networks: the role of contact structure. Proc Biol Sci. 2003 Apr 7;270(1516):699–708. doi: 10.1098/rspb.2002.2305. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Rothenberg R. B., Potterat J. J., Woodhouse D. E., Muth S. Q., Darrow W. W., Klovdahl A. S. Social network dynamics and HIV transmission. AIDS. 1998 Aug 20;12(12):1529–1536. doi: 10.1097/00002030-199812000-00016. [DOI] [PubMed] [Google Scholar]
  12. Walker Polly R., Worobey Michael, Rambaut Andrew, Holmes Edward C., Pybus Oliver G. Epidemiology: Sexual transmission of HIV in Africa. Nature. 2003 Apr 17;422(6933):679–679. doi: 10.1038/422679a. [DOI] [PubMed] [Google Scholar]
  13. Watts D. J., Strogatz S. H. Collective dynamics of 'small-world' networks. Nature. 1998 Jun 4;393(6684):440–442. doi: 10.1038/30918. [DOI] [PubMed] [Google Scholar]
  14. Yorke J. A., Hethcote H. W., Nold A. Dynamics and control of the transmission of gonorrhea. Sex Transm Dis. 1978 Apr-Jun;5(2):51–56. doi: 10.1097/00007435-197804000-00003. [DOI] [PubMed] [Google Scholar]

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