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Analysis of a delayed epidemic model with pulse vaccination

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  • Samanta, G.P.

Abstract

In this paper, we have considered a dynamical model of infectious disease that spread by asymptomatic carriers and symptomatically infectious individuals with varying total population size, saturation incidence rate and discrete time delay to become infectious. It is assumed that there is a time lag (τ) to account for the fact that an individual infected with bacteria or virus is not infectious until after some time after exposure. The probability that an individual remains in the latency period (exposed class) at least t time units before becoming infectious is given by a step function with value 1 for 0⩽t⩽τ and value zero for t>τ. The probability that an individual in the latency period has survived is given by e-μτ, where μ denotes the natural mortality rate in all epidemiological classes. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination. We have defined two positive numbers R1 and R2. It is proved that there exists an infection-free periodic solution which is globally attractive if R1<1 and the disease is permanent if R2>1. The important mathematical findings for the dynamical behaviour of the infectious disease model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.

Suggested Citation

  • Samanta, G.P., 2014. "Analysis of a delayed epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 74-85.
    • Handle: RePEc:eee:chsofr:v:66:y:2014:i:c:p:74-85
    DOI: 10.1016/j.chaos.2014.05.008
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Negi, Kuldeep, 2008. "Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 626-638.
    2. Chunjin Wei & Lansun Chen, 2008. "A Delayed Epidemic Model with Pulse Vaccination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-12, March.
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    Cited by:

    1. Napasool Wongvanich & I-Ming Tang & Marc-Antoine Dubois & Puntani Pongsumpun, 2021. "Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand," Mathematics, MDPI, vol. 9(22), pages 1-30, November.

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