IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v139y2020ics0960077920304343.html
   My bibliography  Save this article

Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model

Author

Listed:
  • Din, Anwarud
  • Khan, Amir
  • Baleanu, Dumitru

Abstract

Similar to other epidemics, the novel coronavirus (COVID-19) spread very fast and infected almost two hundreds countries around the globe since December 2019. The unique characteristics of the COVID-19 include its ability of faster expansion through freely existed viruses or air molecules in the atmosphere. Assuming that the spread of virus follows a random process instead of deterministic. The continuous time Markov Chain (CTMC) through stochastic model approach has been utilized for predicting the impending states with the use of random variables. The proposed study is devoted to investigate a model consist of three exclusive compartments. The first class includes white nose based transmission rate (termed as susceptible individuals), the second one pertains to the infected population having the same perturbation occurrence and the last one isolated (quarantined) individuals. We discuss the model’s extinction as well as the stationary distribution in order to derive the the sufficient criterion for the persistence and disease’ extinction. Lastly, the numerical simulation is executed for supporting the theoretical findings.

Suggested Citation

  • Din, Anwarud & Khan, Amir & Baleanu, Dumitru, 2020. "Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304343
    DOI: 10.1016/j.chaos.2020.110036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920304343
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110036?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. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    2. Lu, Qiuying, 2009. "Stability of SIRS system with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3677-3686.
    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. Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    2. Zhang, Ge & Li, Zhiming & Din, Anwarud & Chen, Tao, 2024. "Dynamic analysis and optimal control of a stochastic COVID-19 model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 498-517.
    3. Yusuf, Abdullahi & Tasiu Mustapha, Umar & Abdulkadir Sulaiman, Tukur & Hincal, Evren & Bayram, Mustafa, 2021. "Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Parsamanesh, Mahmood & Erfanian, Majid, 2021. "Stability and bifurcations in a discrete-time SIVS model with saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Yassine Sabbar & Asad Khan & Anwarud Din, 2022. "Probabilistic Analysis of a Marine Ecological System with Intense Variability," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    7. Marsa Gholamzadeh & Hamidreza Abtahi & Reza Safdari, 2021. "Suggesting a framework for preparedness against the pandemic outbreak based on medical informatics solutions: a thematic analysis," International Journal of Health Planning and Management, Wiley Blackwell, vol. 36(3), pages 754-783, May.
    8. Ogunmiloro, Oluwatayo Michael, 2021. "Mathematical analysis and approximate solution of a fractional order caputo fascioliasis disease model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    10. Amouch, Mohamed & Karim, Noureddine, 2021. "Modeling the dynamic of COVID-19 with different types of transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    11. Yu, Zhenhua & Arif, Robia & Fahmy, Mohamed Abdelsabour & Sohail, Ayesha, 2021. "Self organizing maps for the parametric analysis of COVID-19 SEIRS delayed model," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    12. Zarin, Rahat & Khan, Amir & Inc, Mustafa & Humphries, Usa Wannasingha & Karite, Touria, 2021. "Dynamics of five grade leishmania epidemic model using fractional operator with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    13. Singh, Harendra, 2021. "Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Akgül, Ali, 2023. "Stochastic analysis of a COVID-19 model with effects of vaccination and different transition rates: Real data approach," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    15. Shringi, Sakshi & Sharma, Harish & Rathie, Pushpa Narayan & Bansal, Jagdish Chand & Nagar, Atulya, 2021. "Modified SIRD Model for COVID-19 Spread Prediction for Northern and Southern States of India," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    16. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    17. Babaei, A. & Jafari, H. & Banihashemi, S. & Ahmadi, M., 2021. "Mathematical analysis of a stochastic model for spread of Coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    18. Nikolaos P. Rachaniotis & Thomas K. Dasaklis & Filippos Fotopoulos & Platon Tinios, 2021. "A Two-Phase Stochastic Dynamic Model for COVID-19 Mid-Term Policy Recommendations in Greece: A Pathway towards Mass Vaccination," IJERPH, MDPI, vol. 18(5), pages 1-21, March.
    19. Hussain, Takasar & Aslam, Adnan & Ozair, Muhammad & Tasneem, Fatima & Gómez-Aguilar, J.F., 2021. "Dynamical aspects of pine wilt disease and control measures," Chaos, Solitons & Fractals, Elsevier, vol. 145(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. Muhammad, Yasir & Khan, Nusrat & Awan, Saeed Ehsan & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Kiani, Adiqa Kausar & Ullah, Farman & Shu, Chi-Min, 2022. "Fractional memetic computing paradigm for reactive power management involving wind-load chaos and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2022. "Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    4. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Rastko Jovanović & Miloš Davidović & Ivan Lazović & Maja Jovanović & Milena Jovašević-Stojanović, 2021. "Modelling Voluntary General Population Vaccination Strategies during COVID-19 Outbreak: Influence of Disease Prevalence," IJERPH, MDPI, vol. 18(12), pages 1-18, June.
    6. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    7. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    8. Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    9. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Kumar, Sachin & Cao, Jinde & Abdel-Aty, Mahmoud, 2020. "A novel mathematical approach of COVID-19 with non-singular fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Acedo, L. & González-Parra, Gilberto & Arenas, Abraham J., 2010. "Modal series solution for an epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1151-1157.
    12. Ghanbari, Behzad, 2020. "On forecasting the spread of the COVID-19 in Iran: The second wave," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    13. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    14. Farman, Muhammad & Sarwar, Rabia & Akgul, Ali, 2023. "Modeling and analysis of sustainable approach for dynamics of infections in plant virus with fractal fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    15. Witbooi, Peter J., 2013. "Stability of an SEIR epidemic model with independent stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4928-4936.
    16. Cardoso, Lislaine Cristina & Camargo, Rubens Figueiredo & dos Santos, Fernando Luiz Pio & Dos Santos, José Paulo Carvalho, 2021. "Global stability analysis of a fractional differential system in hepatitis B," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    17. Idris Ahmed & Chanakarn Kiataramkul & Mubarak Muhammad & Jessada Tariboon, 2024. "Existence and Sensitivity Analysis of a Caputo Fractional-Order Diphtheria Epidemic Model," Mathematics, MDPI, vol. 12(13), pages 1-18, June.
    18. Thomas, Neenu & Jana, Arnab & Bandyopadhyay, Santanu, 2022. "Physical distancing on public transport in Mumbai, India: Policy and planning implications for unlock and post-pandemic period," Transport Policy, Elsevier, vol. 116(C), pages 217-236.
    19. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2022. "A computational approach for numerical simulations of the fractal–fractional autoimmune disease model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    20. Babu, N. Ramesh & Balasubramaniam, P., 2022. "Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    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:chsofr:v:139:y:2020:i:c:s0960077920304343. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.