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Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection

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  • He, Shaobo
  • Banerjee, Santo

Abstract

A fractional-order SIR epidemic model is proposed under the influence of both parametric seasonality and the external noise. The integer order SIR epidemic model originally is stable. By introducing seasonality and noise force to the model, behaviors of the system is changed. It is shown that the system has rich dynamical behaviors with different system parameters, fractional derivative order and the degree of seasonality and noise. Complexity of the stochastic model is investigated by using multi-scale fuzzy entropy. Finally, hard limiter controlled system is designed and simulation results show the ratio of infected individuals can converge to a small enough target ρ, which means the epidemic outbreak can be under control by the implementation of some effective medical and health measures.

Suggested Citation

  • He, Shaobo & Banerjee, Santo, 2018. "Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 408-417.
    • Handle: RePEc:eee:phsmap:v:501:y:2018:i:c:p:408-417
    DOI: 10.1016/j.physa.2018.02.045
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    2. Irina Bashkirtseva & Lev Ryashko, 2016. "Noise-induced extinction in Bazykin-Berezovskaya population model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(7), pages 1-8, July.
    3. 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.
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    Cited by:

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    4. Zhuang Wu & Yuanyuan Wang & Jing Gao & Jiayang Song & Yi Zhang, 2022. "A Multistage Time-Delay Control Model for COVID-19 Transmission," Sustainability, MDPI, vol. 14(21), pages 1-23, November.
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    6. Satoh, Daisuke & Uchida, Masato, 2021. "Riccati equation as topology-based model of computer worms and discrete SIR model with constant infectious period," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).

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