IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v501y2018icp408-417.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118301213
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.02.045?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Nabin Sapkota & Atsuo Murata & Waldemar Karwowski & Mohammad Reza Davahli & Krzysztof Fiok & Awad M. Aljuaid & Tadeusz Marek & Tareq Ahram, 2022. "The Chaotic Behavior of the Spread of Infection during the COVID-19 Pandemic in Japan," IJERPH, MDPI, vol. 19(19), pages 1-16, October.
    3. 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).
    4. Yan, Bo & Palit, Sanjay K. & Mukherjee, Sayan & Banerjee, Santo, 2019. "Signature of complexity in time–frequency domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    5. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhou, Xueyong & Shi, Xiangyun & Wei, Ming, 2022. "Dynamical behavior and optimal control of a stochastic mathematical model for cholera," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    3. Hattaf, Khalid & Mahrouf, Marouane & Adnani, Jihad & Yousfi, Noura, 2018. "Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 591-600.
    4. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Liu, Liya & Hu, Jingwei, 2020. "Analysis of a hybrid switching SVIR epidemic model with vaccination and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    5. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    6. Shibing You & Hengli Wang & Miao Zhang & Haitao Song & Xiaoting Xu & Yongzeng Lai, 2020. "Assessment of monthly economic losses in Wuhan under the lockdown against COVID-19," Palgrave Communications, Palgrave Macmillan, vol. 7(1), pages 1-12, December.
    7. Verma, Tina & Gupta, Arvind Kumar, 2020. "Mean-field dispersal induced synchrony and stability in an epidemic model under patchy environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    8. Liu, Qiong & Zhang, Meng & Chen, Lansun, 2019. "State feedback impulsive therapy to SIS model of animal infectious diseases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 222-232.
    9. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    10. Liu, Chao & Wang, Luping & Zhang, Qingling & Yan, Yun, 2017. "Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 682-698.
    11. Nguyen, Dang H. & Nguyen, Nhu N. & Yin, George, 2021. "Stochastic functional Kolmogorov equations, I: Persistence," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 319-364.
    12. Liu, Chao & Yu, Longfei & Zhang, Qingling & Li, Yuanke, 2018. "Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 115-137.
    13. Sun, Shulin & Zhang, Xiaofeng, 2018. "Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 38-56.
    14. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Chen, Shihua, 2020. "A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    15. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.
    16. Liu, Chao & Wang, Luping & Zhang, Qingling & Li, Yuanke, 2018. "Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1216-1239.
    17. Xin, Ming-Zhen & Wang, Bin-Guo, 2020. "Stationary distribution and extinction of a stochastic tuberculosis model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    18. Liu, Guodong & Meng, Xinzhu, 2019. "Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    19. Zhang, Beibei & Wang, Hangying & Lv, Guangying, 2018. "Exponential extinction of a stochastic predator–prey model with Allee effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 192-204.
    20. Jia, Fangju & Lv, Guangying, 2018. "Dynamic analysis of a stochastic rumor propagation model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 613-623.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:501:y:2018:i:c:p:408-417. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.