IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v193y2022icp32-56.html
   My bibliography  Save this article

Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes

Author

Listed:
  • Hoang, Manh Tuan

Abstract

In this work, we propose and analyze nonstandard finite difference (NSFD) schemes for an improved hepatitis B virus (HBV) model. Dynamical properties of the constructed NSFD schemes are studied rigorously. It is proven that the NSFD schemes preserve positivity, boundedness and asymptotic stability of the HBV model for all finite step sizes. In addition, convergence and error bounds for the NSFD schemes are also investigated. The theoretical results and advantages of the NSFD schemes over some existing standard finite difference ones are supported and illustrated by a set of numerical examples. The numerical results show that some typical standard numerical schemes cannot preserve the dynamics of the continuous model for some given step sizes; consequently, they generate numerical solutions that are not only unstable but also negative. Conversely, the constructed NSFD schemes preserve the essential mathematical features of the continuous model for any finite step size; therefore, they are suitable to simulate the dynamics of the HBV model over long time intervals.

Suggested Citation

  • Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:32-56
    DOI: 10.1016/j.matcom.2021.09.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421003499
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.09.020?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. Gao, Fei & Li, Xiling & Li, Wenqin & Zhou, Xianjin, 2021. "Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. 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).
    3. Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
    4. Garba, S.M. & Gumel, A.B. & Hassan, A.S. & Lubuma, J.M.-S., 2015. "Switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 388-403.
    5. Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "On the analysis of semi-analytical solutions of Hepatitis B epidemic model under the Caputo-Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Wood, Daniel T. & Kojouharov, Hristo V. & Dimitrov, Dobromir T., 2017. "Universal approaches to approximate biological systems with nonstandard finite difference methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 337-350.
    7. Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.
    8. Sweilam, Nasser Hassan & El-Sayed, Adel Abd Elaziz & Boulaaras, Salah, 2021. "Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    9. Adamu, Elias M. & Patidar, Kailash C. & Ramanantoanina, Andriamihaja, 2021. "An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 171-190.
    10. Khalsaraei, Mohammad Mehdizadeh & Shokri, Ali & Ramos, Higinio & Heydari, Shahin, 2021. "A positive and elementary stable nonstandard explicit scheme for a mathematical model of the influenza disease," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 397-410.
    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. Hoang, Manh Tuan, 2022. "Positivity and boundedness preserving nonstandard finite difference schemes for solving Volterra’s population growth model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 359-373.
    2. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.

    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. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.
    2. Hoang, Manh Tuan, 2022. "Positivity and boundedness preserving nonstandard finite difference schemes for solving Volterra’s population growth model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 359-373.
    3. Pasha, Syed Ahmed & Nawaz, Yasir & Arif, Muhammad Shoaib, 2023. "On the nonstandard finite difference method for reaction–diffusion models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Yaagoub, Zakaria & Allali, Karam, 2022. "Fractional HBV infection model with both cell-to-cell and virus-to-cell transmissions and adaptive immunity," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Carlos Julio Mayorga & María Ángeles Castro & Antonio Sirvent & Francisco Rodríguez, 2023. "On the Construction of Exact Numerical Schemes for Linear Delay Models," Mathematics, MDPI, vol. 11(8), pages 1-9, April.
    6. Agus Suryanto & Isnani Darti & Syaiful Anam, 2017. "Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-9, May.
    7. 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.
    8. Eva Kaslik & Mihaela Neamţu & Loredana Flavia Vesa, 2021. "Global Stability Analysis of a Five-Dimensional Unemployment Model with Distributed Delay," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    9. Ghanbari, Behzad, 2021. "On detecting chaos in a prey-predator model with prey’s counter-attack on juvenile predators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. García, M.A. & Castro, M.A. & Martín, J.A. & Rodríguez, F., 2018. "Exact and nonstandard numerical schemes for linear delay differential models," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 337-345.
    11. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    12. Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Higinio Ramos & Shao-Wen Yao & Maryam Molayi, 2022. "Efficient Numerical Solutions to a SIR Epidemic Model," Mathematics, MDPI, vol. 10(18), pages 1-15, September.
    13. Hennie Husniah & Ruhanda Ruhanda & Asep K. Supriatna & Md. H. A. Biswas, 2021. "SEIR Mathematical Model of Convalescent Plasma Transfusion to Reduce COVID-19 Disease Transmission," Mathematics, MDPI, vol. 9(22), pages 1-16, November.
    14. Khan, Aziz & Gómez-Aguilar, J.F. & Saeed Khan, Tahir & Khan, Hasib, 2019. "Stability analysis and numerical solutions of fractional order HIV/AIDS model," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 119-128.
    15. Iqbal, Zafar & Ahmed, Nauman & Baleanu, Dumitru & Adel, Waleed & Rafiq, Muhammad & Aziz-ur Rehman, Muhammad & Alshomrani, Ali Saleh, 2020. "Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    16. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    17. Shah, Kamal & Abdeljawad, Thabet & Ud Din, Rahim, 2022. "To study the transmission dynamic of SARS-CoV-2 using nonlinear saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    18. Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Samad Noeiaghdam & Maryam Molayi, 2021. "Nonstandard Finite Difference Schemes for an SIR Epidemic Model," Mathematics, MDPI, vol. 9(23), pages 1-13, November.
    19. Omame, Andrew & Abbas, Mujahid & Abdel-Aty, Abdel-Haleem, 2022. "Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    20. Tri Nguyen-Huu & Pierre Auger & Ali Moussaoui, 2023. "On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect," Mathematics, MDPI, vol. 11(13), pages 1-25, June.

    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:matcom:v:193:y:2022:i:c:p:32-56. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.