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Proceedings of the Royal Society B: Biological Sciences logoLink to Proceedings of the Royal Society B: Biological Sciences
. 2004 Dec 7;271(1556):2431–2438. doi: 10.1098/rspb.2004.2877

The impact of cross-immunity, mutation and stochastic extinction on pathogen diversity.

Laith J Abu-Raddad 1, Neil M Ferguson 1
PMCID: PMC1691886  PMID: 15590592

Abstract

We examine the dynamics of antigenically diverse infectious agents using a mathematical model describing the transmission dynamics of arbitrary numbers of pathogen strains, interacting via cross-immunity, and in the presence of mutations generating new strains and stochastic extinctions of existing ones. Equilibrium dynamics fall into three classes depending on cross-immunity, transmissibility and host population size: systems where global extinction is likely, stable single-strain persistence, and multiple-strain persistence with stable diversity. Where multi-strain dynamics are stable, a diversity threshold region separates a low-prevalence, low-diversity region of parameter space from a high-diversity, high-prevalence region. The location of the threshold region is determined by the reproduction number of the pathogen and the intensity of cross-immunity, with the sharpness of the transition being determined by the manner in which immunity accrues with repeated infections. Host population size and cross-immunity are found to be the most decisive factors in determining pathogen diversity. While the model framework developed is simplified, we show that it can capture essential aspects of the complex evolutionary dynamics of pathogens such as influenza.

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Selected References

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  1. Ackerman E., Longini I. M., Jr, Seaholm S. K., Hedin A. S. Simulation of mechanisms of viral interference in influenza. Int J Epidemiol. 1990 Jun;19(2):444–454. doi: 10.1093/ije/19.2.444. [DOI] [PubMed] [Google Scholar]
  2. Andreasen V., Lin J., Levin S. A. The dynamics of cocirculating influenza strains conferring partial cross-immunity. J Math Biol. 1997 Aug;35(7):825–842. doi: 10.1007/s002850050079. [DOI] [PubMed] [Google Scholar]
  3. Black F. L. Measles endemicity in insular populations: critical community size and its evolutionary implication. J Theor Biol. 1966 Jul;11(2):207–211. doi: 10.1016/0022-5193(66)90161-5. [DOI] [PubMed] [Google Scholar]
  4. Castillo-Chavez C., Hethcote H. W., Andreasen V., Levin S. A., Liu W. M. Epidemiological models with age structure, proportionate mixing, and cross-immunity. J Math Biol. 1989;27(3):233–258. doi: 10.1007/BF00275810. [DOI] [PubMed] [Google Scholar]
  5. Cooper B. S. Pathogen population dynamics: the age of the strain. Trends Microbiol. 2001 May;9(5):199–200. doi: 10.1016/s0966-842x(01)02034-0. [DOI] [PubMed] [Google Scholar]
  6. Dawes J. H. P., Gog J. R. The onset of oscillatory dynamics in models of multiple disease strains. J Math Biol. 2002 Dec;45(6):471–510. doi: 10.1007/s00285-002-0163-9. [DOI] [PubMed] [Google Scholar]
  7. Ferguson Neil M., Galvani Alison P., Bush Robin M. Ecological and immunological determinants of influenza evolution. Nature. 2003 Mar 27;422(6930):428–433. doi: 10.1038/nature01509. [DOI] [PubMed] [Google Scholar]
  8. Gog J. R., Swinton J. A status-based approach to multiple strain dynamics. J Math Biol. 2002 Feb;44(2):169–184. doi: 10.1007/s002850100120. [DOI] [PubMed] [Google Scholar]
  9. Grenfell Bryan T., Pybus Oliver G., Gog Julia R., Wood James L. N., Daly Janet M., Mumford Jenny A., Holmes Edward C. Unifying the epidemiological and evolutionary dynamics of pathogens. Science. 2004 Jan 16;303(5656):327–332. doi: 10.1126/science.1090727. [DOI] [PubMed] [Google Scholar]
  10. Gupta S., Ferguson N., Anderson R. Chaos, persistence, and evolution of strain structure in antigenically diverse infectious agents. Science. 1998 May 8;280(5365):912–915. doi: 10.1126/science.280.5365.912. [DOI] [PubMed] [Google Scholar]
  11. Gupta S., Maiden M. C. Exploring the evolution of diversity in pathogen populations. Trends Microbiol. 2001 Apr;9(4):181–185. doi: 10.1016/s0966-842x(01)01986-2. [DOI] [PubMed] [Google Scholar]
  12. Gupta S., Maiden M. C., Feavers I. M., Nee S., May R. M., Anderson R. M. The maintenance of strain structure in populations of recombining infectious agents. Nat Med. 1996 Apr;2(4):437–442. doi: 10.1038/nm0496-437. [DOI] [PubMed] [Google Scholar]
  13. Gupta S., Trenholme K., Anderson R. M., Day K. P. Antigenic diversity and the transmission dynamics of Plasmodium falciparum. Science. 1994 Feb 18;263(5149):961–963. doi: 10.1126/science.8310293. [DOI] [PubMed] [Google Scholar]
  14. Lin J., Andreasen V., Levin S. A. Dynamics of influenza A drift: the linear three-strain model. Math Biosci. 1999 Nov-Dec;162(1-2):33–51. doi: 10.1016/s0025-5564(99)00042-5. [DOI] [PubMed] [Google Scholar]
  15. May R. M., Nowak M. A. Coinfection and the evolution of parasite virulence. Proc Biol Sci. 1995 Aug 22;261(1361):209–215. doi: 10.1098/rspb.1995.0138. [DOI] [PubMed] [Google Scholar]
  16. May R. M., Nowak M. A. Superinfection, metapopulation dynamics, and the evolution of diversity. J Theor Biol. 1994 Sep 7;170(1):95–114. doi: 10.1006/jtbi.1994.1171. [DOI] [PubMed] [Google Scholar]
  17. Nowak M. A., May R. M. Superinfection and the evolution of parasite virulence. Proc Biol Sci. 1994 Jan 22;255(1342):81–89. doi: 10.1098/rspb.1994.0012. [DOI] [PubMed] [Google Scholar]
  18. Simonsen L., Clarke M. J., Schonberger L. B., Arden N. H., Cox N. J., Fukuda K. Pandemic versus epidemic influenza mortality: a pattern of changing age distribution. J Infect Dis. 1998 Jul;178(1):53–60. doi: 10.1086/515616. [DOI] [PubMed] [Google Scholar]

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