IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v147y2021ics0960077921003374.html
   My bibliography  Save this article

Time-dependent probability distribution for number of infection in a stochastic SIS model: case study COVID-19

Author

Listed:
  • Otunuga, Olusegun Michael

Abstract

We derive the time-dependent probability distribution for the number of infected individuals at a given time in a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model. The mean, variance, skewness, and kurtosis of the distribution are obtained as a function of time. We study the effect of noise intensity on the distribution and later derive and analyze the effect of changes in the transmission and recovery rates of the disease. Our analysis reveals that the time-dependent probability density function exists if the basic reproduction number is greater than one. It converges to the Dirac delta function on the long run (entirely concentrated on zero) as the basic reproduction number tends to one from above. The result is applied using published COVID-19 parameters and also applied to analyze the probability distribution of the aggregate number of COVID-19 cases in the United States for the period: January 22, 2020-March 23, 2021. Findings show that the distribution shifts concentration to the right until it concentrates entirely on the carrying infection capacity as the infection growth rate increases or the recovery rate reduces. The disease eradication and disease persistence thresholds are calculated.

Suggested Citation

  • Otunuga, Olusegun Michael, 2021. "Time-dependent probability distribution for number of infection in a stochastic SIS model: case study COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003374
    DOI: 10.1016/j.chaos.2021.110983
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921003374
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110983?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. Memon, Zaibunnisa & Qureshi, Sania & Memon, Bisharat Rasool, 2021. "Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. 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).
    3. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Pelinovsky, Efim & Kurkin, Andrey & Kurkina, Oxana & Kokoulina, Maria & Epifanova, Anastasia, 2020. "Logistic equation and COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Wang, Peipei & Zheng, Xinqi & Li, Jiayang & Zhu, Bangren, 2020. "Prediction of epidemic trends in COVID-19 with logistic model and machine learning technics," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Zhang, Xiao-Bing & Chang, Suqin & Shi, Qihong & Huo, Hai-Feng, 2018. "Qualitative study of a stochastic SIS epidemic model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 805-817.
    8. Abdullah, & Ahmad, Saeed & Owyed, Saud & Abdel-Aty, Abdel-Haleem & Mahmoud, Emad E. & Shah, Kamal & Alrabaiah, Hussam, 2021. "Mathematical analysis of COVID-19 via new mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    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. Javier Cifuentes-Faura & Ursula Faura-Martínez & Matilde Lafuente-Lechuga, 2022. "Mathematical Modeling and the Use of Network Models as Epidemiological Tools," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    2. Tatsukawa, Yuichi & Arefin, Md. Rajib & Utsumi, Shinobu & Kuga, Kazuki & Tanimoto, Jun, 2022. "Stochasticity of disease spreading derived from the microscopic simulation approach for various physical contact networks," Applied Mathematics and Computation, Elsevier, vol. 431(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. Batabyal, Saikat, 2021. "COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Amouch, Mohamed & Karim, Noureddine, 2021. "Modeling the dynamic of COVID-19 with different types of transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Paul, Ayan & Reja, Selim & Kundu, Sayani & Bhattacharya, Sabyasachi, 2021. "COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Abdullah, & Ahmad, Saeed & Owyed, Saud & Abdel-Aty, Abdel-Haleem & Mahmoud, Emad E. & Shah, Kamal & Alrabaiah, Hussam, 2021. "Mathematical analysis of COVID-19 via new mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Memon, Zaibunnisa & Qureshi, Sania & Memon, Bisharat Rasool, 2021. "Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    7. Trikha, Pushali & Mahmoud, Emad E. & Jahanzaib, Lone Seth & Matoog, R.T. & Abdel-Aty, Mahmoud, 2021. "Fractional order biological snap oscillator: Analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. 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.
    9. Wang, Peipei & Zheng, Xinqi & Ai, Gang & Liu, Dongya & Zhu, Bangren, 2020. "Time series prediction for the epidemic trends of COVID-19 using the improved LSTM deep learning method: Case studies in Russia, Peru and Iran," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Fadaki, Masih & Asadikia, Atie, 2024. "Augmenting Monte Carlo Tree Search for managing service level agreements," International Journal of Production Economics, Elsevier, vol. 271(C).
    11. Masum, Mohammad & Masud, M.A. & Adnan, Muhaiminul Islam & Shahriar, Hossain & Kim, Sangil, 2022. "Comparative study of a mathematical epidemic model, statistical modeling, and deep learning for COVID-19 forecasting and management," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    12. Perrier, Frédéric & Girault, Frédéric, 2022. "Scaling and fine structure of superstable periodic orbits in the logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    13. Basnarkov, Lasko, 2021. "SEAIR Epidemic spreading model of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    14. 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.
    15. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    16. Yifeng Liu & Yuan Lai, 2024. "Analyzing jogging activity patterns and adaptation to public health regulation," Environment and Planning B, , vol. 51(3), pages 670-688, March.
    17. Mishra, A.M. & Purohit, S.D. & Owolabi, K.M. & Sharma, Y.D., 2020. "A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    18. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    19. Calatayud, Julia & Jornet, Marc & Mateu, Jorge & Pinto, Carla M.A., 2023. "A new population model for urban infestations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    20. Ullah, Mohammad Sharif & Higazy, M. & Kabir, K.M. Ariful, 2022. "Dynamic analysis of mean-field and fractional-order epidemic vaccination strategies by evolutionary game approach," 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:147:y:2021:i:c:s0960077921003374. 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.