IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2707-d664173.html
   My bibliography  Save this article

Dynamics of Tumor-Immune System with Random Noise

Author

Listed:
  • Fathalla A. Rihan

    (Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, United Arab Emirates)

  • Chinnathambi Rajivganthi

    (School of Applied Mathematics, Getulio Vargas Foundation, Rio de Janeiro 22250-900, Brazil)

Abstract

With deterministic differential equations, we can understand the dynamics of tumor-immune interactions. Cancer-immune interactions can, however, be greatly disrupted by random factors, such as physiological rhythms, environmental factors, and cell-to-cell communication. The present study introduces a stochastic differential model in infectious diseases and immunology of the dynamics of a tumor-immune system with random noise. Stationary ergodic distribution of positive solutions to the system is investigated in which the solution fluctuates around the equilibrium of the deterministic case and causes the disease to persist stochastically. In some conditions, it may be possible to attain infection-free status, where diseases die out exponentially with a probability of one. Some numerical simulations are conducted with the Euler–Maruyama scheme in order to verify the results. White noise intensity is a key factor in treating infectious diseases.

Suggested Citation

  • Fathalla A. Rihan & Chinnathambi Rajivganthi, 2021. "Dynamics of Tumor-Immune System with Random Noise," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2707-:d:664173
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2707/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/21/2707/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Xiangdong & Li, Qingze & Pan, Jianxin, 2018. "A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 162-176.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Dynamics of a stochastic tuberculosis model with antibiotic resistance," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 223-230.
    3. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Rihan, F.A. & Abdel Rahman, D.H. & Lakshmanan, S. & Alkhajeh, A.S., 2014. "A time delay model of tumour–immune system interactions: Global dynamics, parameter estimation, sensitivity analysis," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 606-623.
    5. Rihan, F.A. & Lakshmanan, S. & Maurer, H., 2019. "Optimal control of tumour-immune model with time-delay and immuno-chemotherapy," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 147-165.
    6. Yang, Huan & Tan, Yuanshun & Yang, Jin & Liu, Zijian, 2021. "Extinction and persistence of a tumor-immune model with white noise and pulsed comprehensive therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 456-470.
    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. Xu, Changjin & Farman, Muhammad & Akgül, Ali & Nisar, Kottakkaran Sooppy & Ahmad, Aqeel, 2022. "Modeling and analysis fractal order cancer model with effects of chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 161(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. Xu, Changjin & Farman, Muhammad & Akgül, Ali & Nisar, Kottakkaran Sooppy & Ahmad, Aqeel, 2022. "Modeling and analysis fractal order cancer model with effects of chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Duan, Wei-Long & Lin, Ling, 2021. "Noise and delay enhanced stability in tumor-immune responses to chemotherapy system," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Das, Parthasakha & Das, Samhita & Upadhyay, Ranjit Kumar & Das, Pritha, 2020. "Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Das, Parthasakha & Das, Samhita & Das, Pritha & Rihan, Fathalla A. & Uzuntarla, Muhammet & Ghosh, Dibakar, 2021. "Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Zhou, Haihua & Song, Huijuan & Wang, Zejia, 2022. "The effect of time delay in regulatory apoptosis on a tumor model with angiogenesis," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. Liu, Xiangdong & Li, Qingze & Pan, Jianxin, 2018. "A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 162-176.
    8. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    9. Rihan, F.A. & Lakshmanan, S. & Maurer, H., 2019. "Optimal control of tumour-immune model with time-delay and immuno-chemotherapy," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 147-165.
    10. Zhao, Zhong & Pang, Liuyong & Li, Qiuying, 2021. "Analysis of a hybrid impulsive tumor-immune model with immunotherapy and chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    11. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    12. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    13. Shireen Jawad & Matthias Winter & Zain-Aldeen S. A. Rahman & Yasir I. A. Al-Yasir & Anwar Zeb, 2023. "Dynamical Behavior of a Cancer Growth Model with Chemotherapy and Boosting of the Immune System," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
    14. George E. Chatzarakis & Tongxing Li, 2018. "Oscillation Criteria for Delay and Advanced Differential Equations with Nonmonotone Arguments," Complexity, Hindawi, vol. 2018, pages 1-18, April.
    15. Byun, Jong Hyuk & Jung, Il Hyo, 2021. "Phase-specific cancer-immune model considering acquired resistance to therapeutic agents," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    16. Das, Dhiraj Kumar & Kar, T.K., 2021. "Global dynamics of a tuberculosis model with sensitivity of the smear microscopy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    17. Dzyubak, Larysa & Dzyubak, Oleksandr & Awrejcewicz, Jan, 2023. "Nonlinear multiscale diffusion cancer invasion model with memory of states," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    18. R. Rakkiyappan & V. Preethi Latha & Fathalla A. Rihan, 2019. "A Fractional-Order Model for Zika Virus Infection with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-20, November.
    19. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    20. Ndenda, J.P. & Njagarah, J.B.H. & Shaw, S., 2021. "Role of immunotherapy in tumor-immune interaction: Perspectives from fractional-order modelling and sensitivity analysis," Chaos, Solitons & Fractals, Elsevier, vol. 148(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:gam:jmathe:v:9:y:2021:i:21:p:2707-:d:664173. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.