Global stability for a discrete SIR epidemic model with delay in the general incidence function

  • Authors

    • Guiro Aboudramane Département de Mathématique, UFR/ST,Université Nazi Boni, Bobo-Dioulasso, Burkina Faso
    • Dramane Ouedraogo
    • Harouna Ouedraogo
    2019-09-14
    https://doi.org/10.14419/ijamr.v8i2.29528
  • Discrete SIR Epidemic Model, General Incidence, Lyapunov Function, Backward Difference Scheme, Local Stability, Global Stability.
  • In this paper, we construct a backward difference scheme for a class of general SIR epidemic model with general incidence function f. We use the step size h > 0, for the discretization. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, under the conditions that function f satisfies some assumptions. The global stabilities of equilibria are obtained. If the basic reproduction number R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>1, the endemic equilibrium is globally asymptotically stable.

    Author Biography

    • Guiro Aboudramane, Département de Mathématique, UFR/ST,Université Nazi Boni, Bobo-Dioulasso, Burkina Faso

      Département de Mathématiques,

      UFR Sciences et Techniques

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  • How to Cite

    Aboudramane, G., Ouedraogo, D., & Ouedraogo, H. (2019). Global stability for a discrete SIR epidemic model with delay in the general incidence function. International Journal of Applied Mathematical Research, 8(2), 32-45. https://doi.org/10.14419/ijamr.v8i2.29528