IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v159y2019icp161-182.html
   My bibliography  Save this article

Numerical simulations of spread of rabies in a spatially distributed fox population

Author

Listed:
  • Alanazi, Khalaf M.
  • Jackiewicz, Zdzislaw
  • Thieme, Horst R.

Abstract

We describe a numerical algorithm for the simulation of the spread of rabies in a spatially distributed fox population. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. The resulting systems are mixtures of partial differential and integral equations. They are discretized in the space variable by central differences of second order and by the composite trapezoidal rule. In a second step, they are discretized in time by explicit continuous Runge–Kutta methods of fourth order for ordinary and delay differential systems. The results of the numerical calculations are compared for latent periods of fixed and exponentially distributed length and for various proportions of territorial and wandering rabid foxes. The speeds of spread observed in the simulations are compared to spreading speeds obtained by analytic methods and to observed speeds of epizootic frontlines in the European rabies outbreak 1940 to 1980.

Suggested Citation

  • Alanazi, Khalaf M. & Jackiewicz, Zdzislaw & Thieme, Horst R., 2019. "Numerical simulations of spread of rabies in a spatially distributed fox population," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 161-182.
    • Handle: RePEc:eee:matcom:v:159:y:2019:i:c:p:161-182
    DOI: 10.1016/j.matcom.2018.11.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475418303057
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.11.010?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. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    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. Gui-Lai Zhang & Zhi-Yong Zhu & Yu-Chen Wang & Chao Liu, 2024. "Impulsive Discrete Runge–Kutta Methods and Impulsive Continuous Runge–Kutta Methods for Nonlinear Differential Equations with Delayed Impulses," Mathematics, MDPI, vol. 12(19), pages 1-30, September.
    2. Tan, Zengqiang & Zhang, Chengjian, 2022. "Numerical approximation to semi-linear stiff neutral equations via implicit–explicit general linear methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 68-87.
    3. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Qin, Hongyu & Zhang, Qifeng & Wan, Shaohua, 2019. "The continuous Galerkin finite element methods for linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 76-85.
    5. Qin, Tingting & Zhang, Chengjian, 2015. "Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 47-57.
    6. Wang, Qi, 2015. "Numerical oscillation of neutral logistic delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 49-59.
    7. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    8. Xu, Y. & Zhao, J.J., 2008. "Stability of Runge–Kutta methods for neutral delay-integro-differential-algebraic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 571-583.
    9. Amat, Sergio & José Legaz, M. & Pedregal, Pablo, 2015. "A variable step-size implementation of a variational method for stiff differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 49-57.
    10. Cheng, Xue & Chen, Zhong & Zhang, Qingpu, 2015. "An approximate solution for a neutral functional–differential equation with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 27-34.
    11. Zhang, Chengjian & Chen, Hao, 2010. "Asymptotic stability of block boundary value methods for delay differential-algebraic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 100-108.
    12. 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.
    13. M. Motawi Khashan & Rohul Amin & Muhammed I. Syam, 2019. "A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    14. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    15. Tan, Zengqiang & Zhang, Chengjian, 2018. "Implicit-explicit one-leg methods for nonlinear stiff neutral equations," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 196-210.
    16. Zhao, Jingjun & Zhan, Rui & Xu, Yang, 2018. "D-convergence and conditional GDN-stability of exponential Runge–Kutta methods for semilinear delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 45-58.
    17. Bürger, Raimund & Ruiz-Baier, Ricardo & Tian, Canrong, 2017. "Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 28-52.
    18. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
    19. V. Subburayan & N. Ramanujam, 2013. "An Initial Value Technique for Singularly Perturbed Convection–Diffusion Problems with a Negative Shift," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 234-250, July.
    20. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(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:eee:matcom:v:159:y:2019:i:c:p:161-182. 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.