IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3756-d940409.html
   My bibliography  Save this article

Stochastic Analysis of a Hantavirus Infection Model

Author

Listed:
  • Yousef Alnafisah

    (Department of Mathematics, College of Sciences, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia)

  • Moustafa El-Shahed

    (Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, P.O. Box 3771, Unaizah 51911, Saudi Arabia)

Abstract

In this paper, a stochastic Hantavirus infection model is constructed. The existence, uniqueness, and boundedness of the positive solution of the stochastic Hantavirus infection model are derived. The conditions for the extinction of the Hantavirus infection from the stochastic system are obtained. Furthermore, the criteria for the presence of a unique ergodic stationary distribution for the Hantavirus infection model are established using a suitable Lyapunov function. Finally, the importance of environmental noise in the Hantavirus infection model is illustrated using the Milstein method.

Suggested Citation

  • Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3756-:d:940409
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3756/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3756/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li, Qiuyue & Cong, Fuzhong & Liu, Tianbao & Zhou, Yaoming, 2020. "Stationary distribution of a stochastic HIV model with two infective stages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    2. Fauzi Mohamed Yusof & Farah Aini Abdullah & Ahmad Izani Md. Ismail, 2019. "Modeling and Optimal Control on the Spread of Hantavirus Infection," Mathematics, MDPI, vol. 7(12), pages 1-11, December.
    3. Mu, Yu & Lo, Wing-Cheong, 2021. "Stochastic dynamics of populations with refuge in polluted turbidostat," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    5. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Wang, Zhaojuan & Deng, Meiling & Liu, Meng, 2021. "Stationary distribution of a stochastic ratio-dependent predator-prey system with regime-switching," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Taki-Eddine Oussaeif & Shaher Momani, 2022. "A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    8. Chunyan Ji & Daqing Jiang & Hong Liu & Qingshan Yang, 2010. "Existence, Uniqueness and Ergodicity of Positive Solution of Mutualism System with Stochastic Perturbation," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-18, July.
    Full references (including those not matched with items on IDEAS)

    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. Huyi Wang & Ge Zhang & Tao Chen & Zhiming Li, 2023. "Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence," Mathematics, MDPI, vol. 11(7), pages 1-17, April.
    2. Zhao, Xin & Liu, Lidan & Liu, Meng & Fan, Meng, 2024. "Stochastic dynamics of coral reef system with stage-structure for crown-of-thorns starfish," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Benazzouz, Meryem & Caraballo, Tomás & El Fatini, Mohamed & Laaribi, Aziz, 2024. "Discontinuous stochastic modeling and discrete numerical approximation for Tuberculosis model with relapse," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Wu, Shuying & Yuan, Sanling & Lan, Guijie & Zhang, Tonghua, 2024. "Understanding the dynamics of hepatitis B transmission: A stochastic model with vaccination and Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    5. Sayed Murad Ali Shah & Yufeng Nie & Anwarud Din & Abdulwasea Alkhazzan, 2024. "Dynamics of Hepatitis B Virus Transmission with a Lévy Process and Vaccination Effects," Mathematics, MDPI, vol. 12(11), pages 1-24, May.
    6. Juan Liu & Jie Hu & Peter Yuen & Fuzhong Li, 2022. "A Seasonally Competitive M-Prey and N-Predator Impulsive System Modeled by General Functional Response for Integrated Pest Management," Mathematics, MDPI, vol. 10(15), pages 1-15, July.
    7. Xu, Libai & Kong, Dehan & Wang, Lidan & Gu, Hong & Kenney, Toby & Xu, Ximing, 2023. "Proportional stochastic generalized Lotka–Volterra model with an application to learning microbial community structures," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    8. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    9. Isra Al-Shbeil & Noureddine Djenina & Ali Jaradat & Abdallah Al-Husban & Adel Ouannas & Giuseppe Grassi, 2023. "A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    10. Abdallah Al-Husban & Noureddine Djenina & Rania Saadeh & Adel Ouannas & Giuseppe Grassi, 2023. "A New Incommensurate Fractional-Order COVID 19: Modelling and Dynamical Analysis," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    11. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    12. Din, Anwarud, 2024. "Bifurcation analysis of a delayed stochastic HBV epidemic model: Cell-to-cell transmission," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    13. Tan, Yiping & Cai, Yongli & Sun, Xiaodan & Wang, Kai & Yao, Ruoxia & Wang, Weiming & Peng, Zhihang, 2022. "A stochastic SICA model for HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    14. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    15. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    16. Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    17. Han, Bingtao & Jiang, Daqing & Zhou, Baoquan & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    18. Lu, Chun, 2022. "Dynamical analysis and numerical simulations on a crowley-Martin predator-prey model in stochastic environment," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    19. Rao, Feng & Luo, Junling, 2021. "Stochastic effects on an HIV/AIDS infection model with incomplete diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    20. Tingting Xue & Xiaolin Fan & Yan Xu, 2023. "Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.

    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:10:y:2022:i:20:p:3756-:d:940409. 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.