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    Computation of the domain of attraction for suboptimal immunity epidemic models using the maximal Lyapunov function method

    193310_97599_Abstrace-Applied_Analys-508794.pdf (2.417Mb)
    Access Status
    Open access
    Authors
    Phang, C.
    Wu, Yong Hong
    Wiwatanapataphee, Benchawan
    Date
    2013
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Phang, Chang and Wu, Yonghong and Wiwatanapataphee, Benchawan. 2013. Computation of the domain of attraction for suboptimal immunity epidemic models using the maximal Lyapunov function method. Abstract and Applied Analysis. 2013 (508794); pp. 1-7.
    Source Title
    Abstract and Applied Analysis
    DOI
    10.1155/2013/508794
    ISSN
    1085-3375
    Remarks

    This article is published under the Open Access publishing model and distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/. Please refer to the licence to obtain terms for any further reuse or distribution of this work.

    URI
    http://hdl.handle.net/20.500.11937/23210
    Collection
    • Curtin Research Publications
    Abstract

    We are concerned with the estimation of the domain of attraction (DOA) for suboptimal immunity epidemic models. We establish a procedure to determine the maximal Lyapunov function in the form of rational functions. Based on the definition of DOA and the maximal Lyapunov function, a theorem and subsequently a numerical procedure are established to determine the maximal Lyapunov function and the DOA. Determination of the domain of attraction for epidemic models is very important for understanding the dynamic behaviour of the disease transmission as a function of the state of population distribution in different categories of disease states. We focus on suboptimal immunity epidemic models with saturated treatment rate and nonlinear incidence rate. Different from classical models, suboptimal immunity models are more realistic to explain the microparasite infection diseases such as Pertussis and Influenza A. We show that, for certain values of the parameter, larger k value (i.e., the model is more toward the SIR model) leads to a smaller DOA.

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