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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

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Abstract

An SI 1 I 2 RS epidemic model is studied. We derive the sufficient conditions on the system parameters which guarantee that the equilibrium points of the system are locally asymptotically stable or globally asymptotically stable.

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References

  1. Barnett, S., Cameron, R.G.: Introduction to Mathematical Control Theory. University of Bradford (1985)

    Google Scholar 

  2. Beltraml, E.: Mathematics for Dynamic Modeling. State University of New York (1998)

    Google Scholar 

  3. Beretta, E., Takeuchi, Y.S.: Global stability of an SIR epidemic model with time delays. J.Math. Biol. 40, 250–260 (1995)

    MathSciNet  Google Scholar 

  4. Blyuss, K.B., Kyrychko, Y.N.: On a basic model of a two-disease epidemic. Appl. Math. Comput. 160, 177–187 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cooke, K.L., vanden Driessche, P.: Analysis of an SEIRS epidemic model with two delays. J.Math. Biol. 35, 240–260 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. De Leon, C.V.: Constructions of Lyapunov functions for classics SIS,SIR and SIRS epidemic model with vairable population size. UNAM, Mexico (2009)

    Google Scholar 

  7. Edelstein - Keshet, L.: Mathematical Models in Biology. Duke University, Random House, New York (1988)

    MATH  Google Scholar 

  8. Hethcote, H.W.: The mathematics of infectious diseases. SIAM Rev. 42, 599–653 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kermack, W.O., McKendrick, A.G.: A contribution tu the Mathematical Theory of Epidemics. P. Soc. London 115, 700–721 (1927)

    MATH  Google Scholar 

  10. Khalil, H.K.: Nonlinear System. Upper Saddle River (1996)

    Google Scholar 

  11. Kyrychko, Y.N., Blyuss, K.B.: Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate. Nonlinear Anal. Real World Appl. 6, 495–507 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, M.Y., Graef, J.R., Wang, L., Karsai, J.: Global dynamics of a SEIR epidemic model with a varying total population size. Math. Biosci. 160, 191–213 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, M.Y., Smith, H.L., Wang, L.: Global dynamics of an SEIR epidemic model with vertical transmission. SIAM J. Appl. Math. 62 (2001)

    Google Scholar 

  14. LsSalle, J.P.: The Stabillity of Dynamic Systems, Philadelphia.PA (1976)

    Google Scholar 

  15. Mena-Lorca, Hethcote, H.W.: Dynamic - models of infections diseases as regulators of population size. J. Math. Biosci. 30, 693–716 (1992)

    MathSciNet  MATH  Google Scholar 

  16. Thieme, H.R., Castillo-Chavez, C.: The role of variable infectivity in the human immumodeficiency virus epidemic. In: Engineering materials, pp. 157–177. Springer, Heidelberg (1989)

    Google Scholar 

  17. Wang, L.D., Li, J.Q.: Global stability of an epidemic model with nonlinear incidence rate and differential infectivity. Appl. Math. Comput. 161, 769–778 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Weber, A., Weber, M., Milligan, P.: Modeling epidemics caused by respiratory syncytial virus (RSV). J.Math. Biosci. 172, 95–113 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Dumrongpokaphan, T., Jaihonglam, W., Ouncharoen, R. (2011). Stability of a Two Epidemics Model. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_54

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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