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Stochastic Modeling of Plant Virus Propagation with Biological Control

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  • 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
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    References listed on IDEAS

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    1. Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
    2. 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.
    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. Bellen, Alfredo & Zennaro, Marino, 2013. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780199671373.
    5. 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.
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    Cited by:

    1. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.

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