Stability analysis of an SIR model with immunity and modified transmission function

  • Authors

    • Nidhi Nirwani
    • V.H. Badshah
    • R. Khandelwal
    2015-03-08
    https://doi.org/10.14419/ijamr.v4i2.4257
  • Basic Reproduction Number, Disease Frees Equilibrium, Endemic Equilibrium, Epidemiology, Non-Monotonic Incidence, SIR Model, Stability.

  • Abstract

    This paper examines an SIR epidemic model with a non-monotonic incidence rate. We analyzed the model by considering after infection, only a fraction of transmitted part is shifted to infectious and remaining part gets recovered without becoming infectious. We also analyze the dynamical behavior of the model and derive the stability conditions for the disease-free and the endemic equilibrium. We have found a threshold condition, in terms of basic reproduction number  which is, less than one, the disease free equilibrium is globally attractive and if more than one, the endemic equilibrium exists and is globally stable. We illustrate theoretical results by carrying numerical simulation.

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  • How to Cite

    Nirwani, N., Badshah, V., & Khandelwal, R. (2015). Stability analysis of an SIR model with immunity and modified transmission function. International Journal of Applied Mathematical Research, 4(2), 228-233. https://doi.org/10.14419/ijamr.v4i2.4257

    Received date: 2015-02-01

    Accepted date: 2015-03-02

    Published date: 2015-03-08