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An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise

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  • Alkhazzan, Abdulwasea
  • Wang, Jungang
  • Nie, Yufeng
  • Khan, Hasib
  • Alzabut, Jehad

Abstract

Effective disease control measures are necessary because epidemics have a serious threat to public health. To address this, we propose a novel SVIR epidemic model that highlights the impact of transport-related infection and media coverage, with the inclusion of Lévy noise. With the help of Lyapunov functions and stopping time, we investigate the existence of a positive global solution for the new model. We also derive sufficient conditions for disease extinction as well as persistence. For the validation of our theoretical findings, we develop a numerical scheme to analyze the influence of various parameters on the model’s dynamics. Our findings provide important insight into the science of epidemiology and provide a groundwork for better methods of preventing the spread of disease.

Suggested Citation

  • Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008548
    DOI: 10.1016/j.chaos.2023.113953
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    References listed on IDEAS

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    1. Hussain, Shah & Tunç, Osman & Rahman, Ghaus ur & Khan, Hasib & Nadia, Elissa, 2023. "Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 130-150.
    2. El Fatini, Mohamed & Lahrouz, Aadil & Pettersson, Roger & Settati, Adel & Taki, Regragui, 2018. "Stochastic stability and instability of an epidemic model with relapse," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 326-341.
    3. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar, 2018. "Dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2010-2018.
    4. Xu, Changyong & Li, Xiaoyue, 2018. "The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 227-234.
    5. Ahmad, Shabir & Ullah, Aman & Al-Mdallal, Qasem M. & Khan, Hasib & Shah, Kamal & Khan, Aziz, 2020. "Fractional order mathematical modeling of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Boukanjime, Brahim & Caraballo, Tomás & El Fatini, Mohamed & El Khalifi, Mohamed, 2020. "Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Zhai, Xuanpei & Li, Wenshuang & Wei, Fengying & Mao, Xuerong, 2023. "Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    8. Zhu, Yu & Wang, Liang & Qiu, Zhipeng, 2022. "Dynamics of a stochastic cholera epidemic model with Lévy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    9. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    10. Liu, Junli & Zhou, Yicang, 2009. "Global stability of an SIRS epidemic model with transport-related infection," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 145-158.
    11. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    12. Berrhazi, Badr-eddine & El Fatini, Mohamed & Laaribi, Aziz, 2018. "A stochastic threshold for an epidemic model with Beddington–DeAngelis incidence, delayed loss of immunity and Lévy noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 312-320.
    13. Liu, Ning & Chen, Zhuo & Bao, Guoxian, 2021. "Role of media coverage in mitigating COVID-19 transmission: Evidence from China," Technological Forecasting and Social Change, Elsevier, vol. 163(C).
    14. Defterli, Ozlem, 2021. "Comparative analysis of fractional order dengue model with temperature effect via singular and non-singular operators," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    15. Deepti Muley & Md. Shahin & Charitha Dias & Muhammad Abdullah, 2020. "Role of Transport during Outbreak of Infectious Diseases: Evidence from the Past," Sustainability, MDPI, vol. 12(18), pages 1-22, September.
    16. Kumar, Anuj & Srivastava, Prashant K. & Gupta, R.P., 2019. "Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 77-99.
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