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An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate

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  • Mingming Li
  • Xianning Liu

Abstract

An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions and , respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number .

Suggested Citation

  • Mingming Li & Xianning Liu, 2014. "An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    • Handle: RePEc:hin:jnlaaa:131257
    DOI: 10.1155/2014/131257
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    Cited by:

    1. Phukan, Jyotiska & Dutta, Hemen, 2023. "Dynamic analysis of a fractional order SIR model with specific functional response and Holling type II treatment rate," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Nasir, Hanis, 2022. "On the dynamics of a diabetic population model with two delays and a general recovery rate of complications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 571-602.
    3. Slama, Howida & Hussein, A. & El-Bedwhey, Nabila A. & Selim, Mustafa M., 2019. "An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 144-156.
    4. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Avila-Vales, Eric & Chan-Chí, Noé & García-Almeida, Gerardo, 2014. "Analysis of a viral infection model with immune impairment, intracellular delay and general non-linear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 1-9.

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