2013, 10(3): 705-728. doi: 10.3934/mbe.2013.10.705

Mathematical modeling of citrus groves infected by huanglongbing

1. 

Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, United States, United States, United States

Received  May 2012 Revised  July 2012 Published  April 2013

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.
Citation: Karly Jacobsen, Jillian Stupiansky, Sergei S. Pilyugin. Mathematical modeling of citrus groves infected by huanglongbing. Mathematical Biosciences & Engineering, 2013, 10 (3) : 705-728. doi: 10.3934/mbe.2013.10.705
References:
[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.  doi: 10.1071/AR9780535.  Google Scholar

[2]

USDA Animal and Plant Health Inspection Service, "APHIS News Release: USDA Announces Quarantine to Prevent the Spread of Citrus Disease,", , (2010).   Google Scholar

[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.  doi: 10.2307/2404439.  Google Scholar

[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.  doi: 10.1007/BF02980710.  Google Scholar

[5]

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

[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.  doi: 10.1007/BF02218848.  Google Scholar

[7]

K. Gopalsamy, "Stability and Oscillations in Delay Differential Equations of Population Dynamics,", Kluwer Academic Publishers, (1992).   Google Scholar

[8]

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

[9]

S. E. Halbert, personal communication,, 2010., ().   Google Scholar

[10]

S. E. Halbert, personal communication,, 2012., ().   Google Scholar

[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.   Google Scholar

[12]

A. Hodges and T. Spreen, Economic impacts of citrus greening (hlb) in florida, 2006/07-2010/11,, Food and Resource Economics Department, (2012).   Google Scholar

[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.   Google Scholar

[14]

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

[15]

Texas Department of Agriculture, Texas department of agriculture and USDA confirm detection of plant disease that damages citrus trees,, , (2012).   Google Scholar

[16]

A. Van Bruggen, personal communication,, 2010., ().   Google Scholar

[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.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[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, (1988), 243.   Google Scholar

show all references

References:
[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.  doi: 10.1071/AR9780535.  Google Scholar

[2]

USDA Animal and Plant Health Inspection Service, "APHIS News Release: USDA Announces Quarantine to Prevent the Spread of Citrus Disease,", , (2010).   Google Scholar

[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.  doi: 10.2307/2404439.  Google Scholar

[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.  doi: 10.1007/BF02980710.  Google Scholar

[5]

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

[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.  doi: 10.1007/BF02218848.  Google Scholar

[7]

K. Gopalsamy, "Stability and Oscillations in Delay Differential Equations of Population Dynamics,", Kluwer Academic Publishers, (1992).   Google Scholar

[8]

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

[9]

S. E. Halbert, personal communication,, 2010., ().   Google Scholar

[10]

S. E. Halbert, personal communication,, 2012., ().   Google Scholar

[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.   Google Scholar

[12]

A. Hodges and T. Spreen, Economic impacts of citrus greening (hlb) in florida, 2006/07-2010/11,, Food and Resource Economics Department, (2012).   Google Scholar

[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.   Google Scholar

[14]

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

[15]

Texas Department of Agriculture, Texas department of agriculture and USDA confirm detection of plant disease that damages citrus trees,, , (2012).   Google Scholar

[16]

A. Van Bruggen, personal communication,, 2010., ().   Google Scholar

[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.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[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, (1988), 243.   Google Scholar

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