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Dynamic phenomena arising from an extended Core Group model

Greenhalgh, David and Griffiths, Martin (2009) Dynamic phenomena arising from an extended Core Group model. Mathematical Biosciences, 221 (2). pp. 136-149. ISSN 0025-5564

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    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.

    Item type: Article
    ID code: 14036
    Keywords: epidemic models, equilibrium and stability analysis, basic reproduction number, backward bifurcation, stochastic model, core group model, Mathematics, Agricultural and Biological Sciences(all), Biochemistry, Genetics and Molecular Biology(all), Modelling and Simulation, Applied Mathematics, Statistics and Probability, Immunology and Microbiology(all), Medicine(all)
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science
    Related URLs:
    Depositing user: Mrs Ann Lynch
    Date Deposited: 14 Jan 2010 14:46
    Last modified: 05 Sep 2014 03:57
    URI: http://strathprints.strath.ac.uk/id/eprint/14036

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