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Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate

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  • Gakkhar, Sunita
  • Negi, Kuldeep

Abstract

The impulsive vaccination strategy is applied to an SIRS epidemic model with non-linear incidence rate. The infection free periodic solution of impulsive system has been obtained and is found to be globally asymptotically stable when R0<1. The supercritical bifurcation occurs at the threshold R0=1. The numerical simulations have been carried out to study the influence of other key parameters. The system shows complex dynamical behavior with respect to the parameter p, the fraction of susceptible that are vaccinated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:3:p:626-638
    DOI: 10.1016/j.chaos.2006.05.054
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    References listed on IDEAS

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    1. Zeng, Guang Zhao & Chen, Lan Sun & Sun, Li Hua, 2005. "Complexity of an SIR epidemic dynamics model with impulsive vaccination control," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 495-505.
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    Cited by:

    1. Park, Hojeong, 2016. "A real option analysis for stochastic disease control and vaccine stockpile policy: An application to H1N1 in Korea," Economic Modelling, Elsevier, vol. 53(C), pages 187-194.
    2. Zhang, Tailei & Teng, Zhidong, 2009. "Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2411-2425.
    3. Jiang, Guirong & Yang, Qigui, 2009. "Complex dynamics in a linear impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2341-2353.
    4. Xu, Rui & Ma, Zhien, 2009. "Stability of a delayed SIRS epidemic model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2319-2325.
    5. Samanta, G.P., 2014. "Analysis of a delayed epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 74-85.
    6. Kim, Hye Kyung & Baek, Hunki, 2013. "The dynamical complexity of a predator–prey system with Hassell–Varley functional response and impulsive effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 1-14.
    7. Imane Abouelkheir & Fadwa El Kihal & Mostafa Rachik & Ilias Elmouki, 2019. "Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity," Mathematics, MDPI, vol. 7(5), pages 1-21, May.
    8. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    9. Jiao, Jianjun & Cai, Shaohong & Li, Limei, 2016. "Impulsive vaccination and dispersal on dynamics of an SIR epidemic model with restricting infected individuals boarding transports," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 145-159.
    10. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.

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