• We are sorry, but NCBI web applications do not support your browser and may not function properly. More information
Logo of procbhomepageaboutsubmitalertseditorial board
Proc Biol Sci. Apr 22, 1999; 266(1421): 859–867.
PMCID: PMC1689913

The effects of local spatial structure on epidemiological invasions.

Abstract

Predicting the likely success of invasions is vitally important in ecology and especially epidemiology. Whether an organism can successfully invade and persist in the short-term is highly dependent on the spatial correlations that develop in the early stages of invasion. By modelling the correlations between individuals, we are able to understand the role of spatial heterogeneity in invasion dynamics without the need for large-scale computer simulations. Here, a natural methodology is developed for modelling the behaviour of individuals in a fixed network. This formulation is applied to the spread of a disease through a structured network to determine invasion thresholds and some statistical properties of a single epidemic.

Full Text

The Full Text of this article is available as a PDF (271K).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Altmann M. Susceptible-infected-removed epidemic models with dynamic partnerships. J Math Biol. 1995;33(6):661–675. [PubMed]
  • Ball F, Nåsell I. The shape of the size distribution of an epidemic in a finite population. Math Biosci. 1994 Oct;123(2):167–181. [PubMed]
  • De Jong MC, Diekmann O, Heesterbeek JA. The computation of R0 for discrete-time epidemic models with dynamic heterogeneity. Math Biosci. 1994 Jan;119(1):97–114. [PubMed]
  • Dickman R. Kinetic phase transitions in a surface-reaction model: Mean-field theory. Phys Rev A. 1986 Nov;34(5):4246–4250. [PubMed]
  • Diekmann O, Heesterbeek JA, Metz JA. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol. 1990;28(4):365–382. [PubMed]
  • Dietz K, Hadeler KP. Epidemiological models for sexually transmitted diseases. J Math Biol. 1988;26(1):1–25. [PubMed]
  • Grenfell BT, Lonergan ME, Harwood J. Quantitative investigations of the epidemiology of phocine distemper virus (PDV) in European common seal populations. Sci Total Environ. 1992 Apr 20;115(1-2):15–29. [PubMed]
  • Islam MN, O'Shaughnessy CD, Smith B. A random graph model for the final-size distribution of household infections. Stat Med. 15(7-9):837–843. [PubMed]
  • Keeling MJ, Grenfell BT. Disease extinction and community size: modeling the persistence of measles. Science. 1997 Jan 3;275(5296):65–67. [PubMed]
  • Keeling MJ, Rand DA, Morris AJ. Correlation models for childhood epidemics. Proc Biol Sci. 1997 Aug 22;264(1385):1149–1156. [PMC free article] [PubMed]
  • Kermack WO, McKendrick AG. Contributions to the mathematical theory of epidemics--I. 1927. Bull Math Biol. 1991;53(1-2):33–55. [PubMed]
  • Levin SA, Durrett R. From individuals to epidemics. Philos Trans R Soc Lond B Biol Sci. 1996 Nov 29;351(1347):1615–1621. [PubMed]
  • Sato K, Matsuda H, Sasaki A. Pathogen invasion and host extinction in lattice structured populations. J Math Biol. 1994;32(3):251–268. [PubMed]
  • Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nature. 1998 Jun 4;393(6684):440–442. [PubMed]

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

Formats:

Related citations in PubMed

See reviews...See all...

Cited by other articles in PMC

See all...

Links

  • PubMed
    PubMed
    PubMed citations for these articles

Recent Activity

Your browsing activity is empty.

Activity recording is turned off.

Turn recording back on

See more...