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      The Fractional SIRC Model and Influenza A

      Author(s): ,
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      Journal: Mathematical Problems in Engineering
      Publisher: Hindawi Limited

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          Abstract

          This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, . We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations.

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          On some Routh–Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rössler, Chua and Chen systems

          E. Ahmed, A.M.A El-Sayed, Hala El-Saka (2006)
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            A fractional-order differential equation model of HIV infection of CD4+ T-cells

            Yongsheng Ding, Haiping Ye (2009)
            Article 0 comments Cited 58 times – based on 0 reviews     Review now
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              The SIRC model and influenza A.

              Philip S. Levin, Viggo Andreasen, Renato Casagrandi … (2006)
              We develop a simple ordinary differential equation model to study the epidemiological consequences of the drift mechanism for influenza A viruses. Improving over the classical SIR approach, we introduce a fourth class (C) for the cross-immune individuals in the population, i.e., those that recovered after being infected by different strains of the same viral subtype in the past years. The SIRC model predicts that the prevalence of a virus is maximum for an intermediate value of R(0), the basic reproduction number. Via a bifurcation analysis of the model, we discuss the effect of seasonality on the epidemiological regimes. For realistic parameter values, the model exhibits a rich variety of behaviors, including chaos and multi-stable periodic outbreaks. Comparison with empirical evidence shows that the simulated regimes are qualitatively and quantitatively consistent with reality, both for tropical and temperate countries. We find that the basins of attraction of coexisting cycles can be fractal sets, thus predictability can in some cases become problematic even theoretically. In accordance with previous studies, we find that increasing cross-immunity tends to complicate the dynamics of the system.
              Article 0 comments Cited 37 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Title: Mathematical Problems in Engineering
                Abbreviated Title: Mathematical Problems in Engineering
                Publisher: Hindawi Limited
                ISSN (Print): 1024-123X
                ISSN (Electronic): 1563-5147
                Publication date Created: 2011
                Publication date (Print): 2011
                Volume: 2011
                Issue:
                Pages: 1-9
                Article
                DOI: 10.1155/2011/480378
                SO-VID: c1ca4bb1-1df3-4c73-b6b8-b812809d9cd1
                Copyright © © 2011
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                http://creativecommons.org/licenses/by/3.0/

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