PMCCPMCCPMCC

Search tips
Search criteria 

Advanced

 
Logo of procbThe Royal Society PublishingProceedings BAboutBrowse by SubjectAlertsFree Trial
 
Proc Biol Sci. 2004 March 22; 271(1539): 625–634.
PMCID: PMC1691637

Frequency-dependent incidence in models of sexually transmitted diseases: portrayal of pair-based transmission and effects of illness on contact behaviour.

Abstract

We explore the transmission process for sexually transmitted diseases (STDs). We derive the classical frequency-dependent incidence mechanistically from a pair-formation model, using an approximation that applies to populations with rapid pairing dynamics (such as core groups or non-pair-bonding animals). This mechanistic derivation provides a framework to assess how accurately frequency-dependent incidence portrays the pair-based transmission known to underlie STD dynamics. This accuracy depends strongly on the disease being studied: frequency-dependent formulations are more suitable for chronic less-transmissible infections than for transient highly transmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes, and we suggest guidelines to help assess under what conditions each class can be appropriately modelled using frequency-dependent incidence. We then extend the derivation to include situations where infected individuals exhibit altered pairing behaviour. For four cases of increasing behavioural complexity, analytic expressions are presented for the generalized frequency-dependent incidence rate, basic reproductive number (R0) and steady-state prevalence (i infinity) of an epidemic. The expression for R0 is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection-induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss the application of our results to STDs (in humans and animals) and other infectious diseases.

Full Text

The Full Text of this article is available as a PDF (213K).

Supplementary Material

Supplementary data file:

Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Able DJ. The contagion indicator hypothesis for parasite-mediated sexual selection. Proc Natl Acad Sci U S A. 1996 Mar 5;93(5):2229–2233. [PubMed]
  • Anderson RM, Garnett GP. Mathematical models of the transmission and control of sexually transmitted diseases. Sex Transm Dis. 2000 Nov;27(10):636–643. [PubMed]
  • Anderson RM, Blythe SP, Gupta S, Konings E. The transmission dynamics of the human immunodeficiency virus type 1 in the male homosexual community in the United Kingdom: the influence of changes in sexual behaviour. Philos Trans R Soc Lond B Biol Sci. 1989 Sep 5;325(1226):45–98. [PubMed]
  • Bauch C, Rand DA. A moment closure model for sexually transmitted disease transmission through a concurrent partnership network. Proc Biol Sci. 2000 Oct 7;267(1456):2019–2027. [PMC free article] [PubMed]
  • Blanchard JF. Populations, pathogens, and epidemic phases: closing the gap between theory and practice in the prevention of sexually transmitted diseases. Sex Transm Infect. 2002 Apr;78 (Suppl 1):i183–i188. [PMC free article] [PubMed]
  • Blower SM, Porco TC, Darby G. Predicting and preventing the emergence of antiviral drug resistance in HSV-2. Nat Med. 1998 Jun;4(6):673–678. [PubMed]
  • Blower SM, Gershengorn HB, Grant RM. A tale of two futures: HIV and antiretroviral therapy in San Francisco. Science. 2000 Jan 28;287(5453):650–654. [PubMed]
  • Boots Michael, Knell Robert J. The evolution of risky behaviour in the presence of a sexually transmitted disease. Proc Biol Sci. 2002 Mar 22;269(1491):585–589. [PMC free article] [PubMed]
  • Bowden FJ, Garnett GP. Trichomonas vaginalis epidemiology: parameterising and analysing a model of treatment interventions. Sex Transm Infect. 2000 Aug;76(4):248–256. [PMC free article] [PubMed]
  • Diekmann O, Dietz K, Heesterbeek JA. The basic reproduction ratio for sexually transmitted diseases: I. Theoretical considerations. Math Biosci. 1991 Dec;107(2):325–339. [PubMed]
  • Dietz K, Hadeler KP. Epidemiological models for sexually transmitted diseases. J Math Biol. 1988;26(1):1–25. [PubMed]
  • Donovan B. The repertoire of human efforts to avoid sexually transmissible diseases: past and present. Part 1: Strategies used before or instead of sex. Sex Transm Infect. 2000 Feb;76(1):7–12. [PMC free article] [PubMed]
  • Ferguson NM, Garnett GP. More realistic models of sexually transmitted disease transmission dynamics: sexual partnership networks, pair models, and moment closure. Sex Transm Dis. 2000 Nov;27(10):600–609. [PubMed]
  • Garnett GP. The geographical and temporal evolution of sexually transmitted disease epidemics. Sex Transm Infect. 2002 Apr;78 (Suppl 1):i14–i19. [PMC free article] [PubMed]
  • Garnett GP. An introduction to mathematical models in sexually transmitted disease epidemiology. Sex Transm Infect. 2002 Feb;78(1):7–12. [PMC free article] [PubMed]
  • Garnett GP, Mertz KJ, Finelli L, Levine WC, St Louis ME. The transmission dynamics of gonorrhoea: modelling the reported behaviour of infected patients from Newark, New Jersey. Philos Trans R Soc Lond B Biol Sci. 1999 Apr 29;354(1384):787–797. [PMC free article] [PubMed]
  • Gold RS, Skinner MJ. Judging a book by its cover: gay men's use of perceptible characteristics to infer antibody status. Int J STD AIDS. 1996 Jan-Feb;7(1):39–43. [PubMed]
  • Hadeler KP, Castillo-Chavez C. A core group model for disease transmission. Math Biosci. 1995 Jul-Aug;128(1-2):41–55. [PubMed]
  • Hamilton WD, Zuk M. Heritable true fitness and bright birds: a role for parasites? Science. 1982 Oct 22;218(4570):384–387. [PubMed]
  • Heesterbeek JA, Metz JA. The saturating contact rate in marriage- and epidemic models. J Math Biol. 1993;31(5):529–539. [PubMed]
  • Hsieh YH, Sheu SP. The effect of density-dependent treatment and behavior change on the dynamics of HIV transmission. J Math Biol. 2001 Jul;43(1):69–80. [PubMed]
  • Kavaliers M, Colwell DD, Choleris E. Parasites and behavior: an ethopharmacological analysis and biomedical implications. Neurosci Biobehav Rev. 1999 Nov;23(7):1037–1045. [PubMed]
  • Kiesecker JM, Skelly DK, Beard KH, Preisser E. Behavioral reduction of infection risk. Proc Natl Acad Sci U S A. 1999 Aug 3;96(16):9165–9168. [PubMed]
  • Kretzschmar M. Sexual network structure and sexually transmitted disease prevention: a modeling perspective. Sex Transm Dis. 2000 Nov;27(10):627–635. [PubMed]
  • Kretzschmar M, Dietz K. The effect of pair formation and variable infectivity on the spread of an infection without recovery. Math Biosci. 1998 Feb;148(1):83–113. [PubMed]
  • Kretzschmar M, Morris M. Measures of concurrency in networks and the spread of infectious disease. Math Biosci. 1996 Apr 15;133(2):165–195. [PubMed]
  • Kretzschmar M, Jager JC, Reinking DP, Van Zessen G, Brouwers H. The basic reproduction ratio R0 for a sexually transmitted disease in a pair formation model with two types of pairs. Math Biosci. 1994 Dec;124(2):181–205. [PubMed]
  • Kretzschmar M, van Duynhoven YT, Severijnen AJ. Modeling prevention strategies for gonorrhea and Chlamydia using stochastic network simulations. Am J Epidemiol. 1996 Aug 1;144(3):306–317. [PubMed]
  • Lockhart AB, Thrall PH, Antonovics J. Sexually transmitted diseases in animals: ecological and evolutionary implications. Biol Rev Camb Philos Soc. 1996 Aug;71(3):415–471. [PubMed]
  • McCallum H, Barlow N, Hone J. How should pathogen transmission be modelled? Trends Ecol Evol. 2001 Jun 1;16(6):295–300. [PubMed]
  • Mertz GJ, Benedetti J, Ashley R, Selke SA, Corey L. Risk factors for the sexual transmission of genital herpes. Ann Intern Med. 1992 Feb 1;116(3):197–202. [PubMed]
  • Newshan G, Taylor B, Gold R. Sexual functioning in ambulatory men with HIV/AIDS. Int J STD AIDS. 1998 Nov;9(11):672–676. [PubMed]
  • Piot P, Bartos M, Ghys PD, Walker N, Schwartländer B. The global impact of HIV/AIDS. Nature. 2001 Apr 19;410(6831):968–973. [PubMed]
  • Schiltz MA, Sandfort TG. HIV-positive people, risk and sexual behaviour. Soc Sci Med. 2000 Jun;50(11):1571–1588. [PubMed]
  • Thrall PH, Antonovics J. Polymorphism in sexual versus non-sexual disease transmission. Proc Biol Sci. 1997 Apr 22;264(1381):581–587. [PMC free article]
  • Webster Joanne P, Hoffman Joseph I, Berdoy Manuel. Parasite infection, host resistance and mate choice: battle of the genders in a simultaneous hermaphrodite. Proc Biol Sci. 2003 Jul 22;270(1523):1481–1485. [PMC free article] [PubMed]

Articles from Proceedings of the Royal Society B: Biological Sciences are provided here courtesy of The Royal Society