IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p456-d504767.html

Stochastic Modeling of Plant Virus Propagation with Biological Control

Author

Listed:
  • Benito Chen-Charpentier

    (Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA)

Abstract

Plants are vital for man and many species. They are sources of food, medicine, fiber for clothes and materials for shelter. They are a fundamental part of a healthy environment. However, plants are subject to virus diseases. In plants most of the virus propagation is done by a vector. The traditional way of controlling the insects is to use insecticides that have a negative effect on the environment. A more environmentally friendly way to control the insects is to use predators that will prey on the vector, such as birds or bats. In this paper we modify a plant-virus propagation model with delays. The model is written using delay differential equations. However, it can also be expressed in terms of biochemical reactions, which is more realistic for small populations. Since there are always variations in the populations, errors in the measured values and uncertainties, we use two methods to introduce randomness: stochastic differential equations and the Gillespie algorithm. We present numerical simulations. The Gillespie method produces good results for plant-virus population models.

Suggested Citation

  • Benito Chen-Charpentier, 2021. "Stochastic Modeling of Plant Virus Propagation with Biological Control," Mathematics, MDPI, vol. 9(5), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:456-:d:504767
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/456/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/456/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
    2. Tongqian Zhang & Xinzhu Meng & Yi Song & Zhenqing Li, 2012. "Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Tongqian Zhang & Xinzhu Meng & Yi Song & Zhenqing Li, 2012. "Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, April.
    4. Haileyesus Tessema Alemneh & Oluwole Daniel Makinde & David Mwangi Theuri, 2019. "Ecoepidemiological Model and Analysis of MSV Disease Transmission Dynamics in Maize Plant," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-14, January.
    5. Bellen, Alfredo & Zennaro, Marino, 2013. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780199671373.
    6. Timo R Maarleveld & Brett G Olivier & Frank J Bruggeman, 2013. "StochPy: A Comprehensive, User-Friendly Tool for Simulating Stochastic Biological Processes," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-10, November.
    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. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.

    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. Wencai Zhao & Tongqian Zhang & Xinzhu Meng & Yang Yang, 2013. "Dynamical Analysis of a Pest Management Model with Saturated Growth Rate and State Dependent Impulsive Effects," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Xiying Wang & Wei Xu & Yujun Cui & Xiaomei Wang, 2014. "Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. El-Sayed, A.M.A. & Rida, S.Z. & Gaber, Y.A., 2020. "Dynamical of curative and preventive treatments in a two-stage plant disease model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Dubey, Balram & Sajan, & Kumar, Ankit, 2021. "Stability switching and chaos in a multiple delayed prey–predator model with fear effect and anti-predator behavior," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 164-192.
    5. Omran, A.K. & Zaky, M.A. & Hendy, A.S. & Pimenov, V.G., 2022. "An easy to implement linearized numerical scheme for fractional reaction–diffusion equations with a prehistorical nonlinear source function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 218-239.
    6. Stephanie S. Johnson & Katelin C. Jackson & Matthew S. Mietchen & Samir Sbai & Elissa J. Schwartz & Eric T. Lofgren, 2021. "Excess Risk of COVID-19 to University Populations Resulting from In-Person Sporting Events," IJERPH, MDPI, vol. 18(16), pages 1-13, August.
    7. N. Peykrayegan & M. Ghovatmand & M. H. Noori Skandari & S. Shateyi, 2025. "Numerical solution of nonlinear fractional delay integro-differential equations with convergence analysis," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(4), pages 1457-1477, December.
    8. S. A. Alharbi & Hegagi M. Ali & Essam M. Elsaid & Mohamed R. Eid & W. S. Hassanin, 2025. "Addressing Various Strategies for Combating the Leaf‐Roll Virus in Potato Plants," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    9. Haileyesus Tessema Alemneh, 2020. "Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    10. Jalal Hajishafieiha & Saeid Abbasbandy, 2022. "Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations," Complexity, John Wiley & Sons, vol. 2022(1).
    11. Berhe Nerea Kahsay & Oluwole D. Makinde, 2023. "Ecoepidemiological Model and Optimal Control Analysis of Tomato Yellow Leaf Curl Virus Disease in Tomato Plant," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    12. Mahmoudi, Fatemeh & Tahmasebi, Mahdieh, 2022. "The convergence of a numerical scheme for additive fractional stochastic delay equations with H>12," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 219-231.
    13. Bo Wang & Jianhua Zhang & Haifeng Guo & Yuwang Zhang & Xiaotuo Qiao, 2016. "Model Study of Information Dissemination in Microblog Community Networks," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    14. James A R Marshall & Andreagiovanni Reina & Thomas Bose, 2019. "Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-16, September.
    15. Fernando Alcántara-López & Carlos Fuentes & Carlos Chávez & Jesús López-Estrada & Fernando Brambila-Paz, 2022. "Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data," Mathematics, MDPI, vol. 10(5), pages 1-18, March.
    16. Debasis Mukherjee, 2022. "Stochastic Analysis of an Eco-Epidemic Model with Biological Control," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2539-2555, December.
    17. Dipty Sharma & Paramjeet Singh, 2020. "Discontinuous Galerkin approximation for excitatory-inhibitory networks with delay and refractory periods," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-25, January.
    18. Banks, H.T. & Banks, J.E. & Bommarco, Riccardo & Laubmeier, A.N. & Myers, N.J. & Rundlöf, Maj & Tillman, Kristen, 2017. "Modeling bumble bee population dynamics with delay differential equations," Ecological Modelling, Elsevier, vol. 351(C), pages 14-23.
    19. Vsevolod G. Sorokin & Andrei V. Vyazmin, 2022. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration," Mathematics, MDPI, vol. 10(11), pages 1-39, May.
    20. Ali, Hegagi Mohamed & Ameen, Ismail Gad & Gaber, Yasmeen Ahmed, 2024. "The effect of curative and preventive optimal control measures on a fractional order plant disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 496-515.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:5:p:456-:d:504767. 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 The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (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.