\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Mathematical modeling of citrus groves infected by huanglongbing

Abstract / Introduction Related Papers Cited by
  • Huanglongbing (citrus greening) is a bacterial disease that is significantly impacting the citrus industry in Florida and poses a risk to the remaining citrus-producing regions of the United States. A mathematical model of a grove infected by citrus greening is developed. An equilibrium stability analysis is presented. The basic reproductive number and its relation to the persistence of the disease is discussed. A numerical study is performed to illustrate the theoretical findings.
    Mathematics Subject Classification: Primary: 92D25, 34D20; Secondary: 92D40.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    R. N. Allen, Epidemiological factors influencing the success of roguing for the control of bunchy top disease of bananas in New South Wales, Australian Journal of Agricultural Research, 29 (1978), 535-544.doi: 10.1071/AR9780535.

    [2]

    USDA Animal and Plant Health Inspection Service, "APHIS News Release: USDA Announces Quarantine to Prevent the Spread of Citrus Disease," http://www.freshfromflorida.com/pi/chrp/greening/citrus_disease-june-2010.pdf. 2010.

    [3]

    M. S. Chan and M. J. Jeger, An analytical model of plant virus disease dynamics with roguing and replanting, Journal of Applied Ecology, 31 (1994), 413-427.doi: 10.2307/2404439.

    [4]

    S. Fishman, R. Marcus, H. Talpaz, M. Bar-Joseph, Y. Oren, R. Salomon and M. Zohar, Epidemiological and economic models for spread and control of citrus tristeza virus disease, Phytoparasitica, 11 (1983), 39-49.doi: 10.1007/BF02980710.

    [5]

    A. Fonda, Uniformly persistent semidynamical systems, Proceedings of the American Mathematical Society, 104 (1988), 111-116.doi: 10.1090/S0002-9939-1988-0958053-2.

    [6]

    H. Freedman, S. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set, Journal of Dynamics and Differential Equations, 6 (1994), 583-600.doi: 10.1007/BF02218848.

    [7]

    K. Gopalsamy, "Stability and Oscillations in Delay Differential Equations of Population Dynamics," Kluwer Academic Publishers, Dordrecht, 1992.

    [8]

    T. Gottwald, Current epidemiological understanding of citrus Huanglongbing, Annual Review of Phytopathology, 48 (2010), 119-139.doi: 10.1146/annurev-phyto-073009-114418.

    [9]

    S. E. Halbert, personal communication, 2010.

    [10]

    S. E. Halbert, personal communication, 2012.

    [11]

    S. E. Halbert and C. K. Manjunath, Asian citrus psyllids (Sternorrhyncha: Psyllidae) and greening disease of citrus: A literature review and assessment of risk in Florida, The Florida Entomologist, 87 (2004), 330-353.

    [12]

    A. Hodges and T. Spreen, Economic impacts of citrus greening (hlb) in florida, 2006/07-2010/11, Food and Resource Economics Department, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida, (2012), http://edis.ifas.ufl.edu/pdffiles/FE/FE90300.pdf.

    [13]

    R. W. H. Pluke, J. A. Qureshi and P. A. Stansly, Citrus flushing patterns, Diaphorina citri (Hemiptera: Psyllidae) populations and parasitism by Tamarixia radiata (Hymenoptera: Eulophidae) in Puerto Rico, The Florida Entomologist, 91 (2008), 36-42.

    [14]

    H. L. Smith and P. Waltman, "The Theory of the Chemostat," Cambridge University Press, Cambridge, 1995.doi: 10.1017/CBO9780511530043.

    [15]

    Texas Department of Agriculture, Texas department of agriculture and USDA confirm detection of plant disease that damages citrus trees, http://www.texasagriculture.gov/RegulatoryPrograms/PlantQuality/PestandDiseaseAlerts/CitrusGreening.aspx, 2012.

    [16]

    A. Van Bruggen, personal communication, 2010.

    [17]

    P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.doi: 10.1016/S0025-5564(02)00108-6.

    [18]

    C. F. Xu, Y. H. Xia, K. B. Li and C. Ke, Further study of the transmission of citrus Huanglongbing by a psyllid, Diaphorina citri Kuwayama, in "Proceedings of the 10th Conference, International Organization of Citrus Virologists" Riverside, California, (1988), 243-248.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(89) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return