Dynamic phenomena arising from an extended Core Group model

David Greenhalgh, Martin Griffiths

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In order to obtain a reasonably accurate model for the spread of a particular infectious disease through a population, it may be necessary for this model to possess some degree of structural complexity. Many such models have, in recent years, been found to exhibit a phenomenon known as backward bifurcation, which generally implies the existence of two subcritical endemic equilibria. It is often possible to refine these models yet further, and we investigate here the influence such a refinement may have on the dynamic behaviour of a system in the region of the parameter space near R0 = 1. We consider a natural extension to a so-called core group model for the spread of a sexually transmitted disease, arguing that this may in fact give rise to a more realistic model. From the deterministic viewpoint we study the possible shapes of the resulting bifurcation diagrams and the associated stability patterns. Stochastic versions of both the original and the extended models are also developed so that the probability of extinction and time to extinction may be examined, allowing us to gain further insights into the complex system dynamics near R0 = 1. A number of interesting phenomena are observed, for which heuristic explanations are provided.
LanguageEnglish
Pages136-149
Number of pages14
JournalMathematical Biosciences
Volume221
Issue number2
DOIs
Publication statusPublished - Oct 2009

Fingerprint

Sexually Transmitted Diseases
Communicable Diseases
Extinction
Model
Population
extinction
Backward Bifurcation
sexually transmitted diseases
Endemic Equilibrium
Infectious Diseases
Bifurcation Diagram
Complex Dynamics
Natural Extension
Psychological Extinction
System Dynamics
Dynamic Behavior
infectious diseases
Parameter Space
Large scale systems
Complex Systems

Keywords

  • epidemic models
  • equilibrium and stability analysis
  • basic reproduction number
  • backward bifurcation
  • stochastic model
  • core group model

Cite this

Greenhalgh, David ; Griffiths, Martin. / Dynamic phenomena arising from an extended Core Group model. In: Mathematical Biosciences. 2009 ; Vol. 221, No. 2. pp. 136-149.
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Dynamic phenomena arising from an extended Core Group model. / Greenhalgh, David; Griffiths, Martin.

In: Mathematical Biosciences, Vol. 221, No. 2, 10.2009, p. 136-149.

Research output: Contribution to journalArticle

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