- Previous Article
- MBE Home
- This Issue
-
Next Article
Global stability of an age-structured cholera model
Mathematical modeling of Glassy-winged sharpshooter population
1. | Department of Mathematics and Statistics, University of Houston - Downtown, Houston, TX 77002, United States, United States |
2. | Department of Natural Sciences, University of Houston - Downtown, Houston, TX 77002, United States |
3. | University of Houston - Downtown, Houston, TX 77002, United States, United States |
4. | Department of Entomology, Texas A&M AgriLife Research, Stephenville, TX 76401, United States |
References:
[1] |
R. Almeida, et al., Vector trasmission of Xylella fastidiosa: Applying fundamental knowledge to generate disease management strategies,, Ann. Entomol. Soc. Am., 98 (2005), 775. Google Scholar |
[2] |
M. Begon, J. Harper and C. Townsend, Ecology: Individuals, Populations and Communities,, 2nd edition, (1990). Google Scholar |
[3] |
M. Blua, P. Philips,and R. A. Redak, A new sharpshooter threatens both crops and ornamentals,, Calif. Agr., 53 (1999), 22.
doi: 10.1094/PHP-2000-0627-01-RS. |
[4] |
S. Choi and N. Koo, Oscillation theory for delay and neutral differential equations,, Trends Math., 2 (1999), 170. Google Scholar |
[5] |
D. R. Causton and J. C. Venus, The Biometry of Plant Growth,, Edward Arnold, (1981).
doi: 10.1111/j.1365-3040.1978.tb00759.x. |
[6] |
J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics,, Lecture Notes in Biomathematics 20, (1977).
|
[7] |
J. De Leon, W. Joses and D. Morgan, Population genetic structure of Homalodisca coagulata (Homoptera: Cicadellidae), the vector of the bacterium Xylella fastidiosa causing Pierce's disease in grapevines,, Ann. Entomol. Soc. Am., 97 (2004), 809. Google Scholar |
[8] |
, ., (). Google Scholar |
[9] |
W. W. Fox, An exponential surplus yield model for optimizing in exploited fish populations,, T. Am. Fish. Soc., 99 (1970), 80.
doi: 10.1577/1548-8659(1970)99<80:AESMFO>2.0.CO;2. |
[10] |
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics,, Mathematics and its Applications 74, (1992).
|
[11] |
J. Grandgirard, G. Roderick, N. Davies, M. S. Hoddle and J. N. Petit, Engineering an invasion: Classical biological control of the glassy-winged sharpshooter, Homalodisca vitripennis, by the egg parasitoid Gonatocerus ashmeadi in Tahiti and Moorea, French Polynesia,, Biol. Invasions, 10 (2008), 135.
doi: 10.1007/s10530-007-9116-y. |
[12] |
N. Hayes, Roots of the transcendendal equation associated with a certain differential difference equation,, J. London Math. Soc., 25 (1950), 226.
doi: 10.1112/jlms/s1-25.3.226. |
[13] |
W. Hewitt, The probable home of Pierce's disease virus,, Plant Dis. Rep., 42 (1958), 211. Google Scholar |
[14] |
C. B. Hutchinson, Circular causal systems in ecology,, Ann. N.Y. Acad. Sci., 50 (1948), 221.
doi: 10.1111/j.1749-6632.1948.tb39854.x. |
[15] |
, ., (). Google Scholar |
[16] |
M. Kot, Elements of Mathematical Ecology,, Cambridge University Press, (2001).
doi: 10.1017/CBO9780511608520. |
[17] |
R. Krugner, J. R. Hagler, J. G. Morse, A. P. Flores, R. L. Groves and M. W. Johnson, Seasonal population dynamics of Homalodisca vitripennis (Hemiptera: Cicadellidae) in sweet orange trees maintained under continuous deficit irrigation,, J. Econ. Entomol., 102 (2009), 960.
doi: 10.1603/029.102.0315. |
[18] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics,, Academic Press, (1993).
|
[19] |
I. M. Lauziére, S. Sheather and F. L. Mitchell, Seasonal abundance and spatio-temporal distribution of dominant xylem fluid-feeding Hemiptera in vineyards of central Texas and surrounding habitats,, Environ. Entomol., 37 (2008), 925. Google Scholar |
[20] |
N. MacDonald, Time Lags in Biological Models,, Lecture Notes in Biomathematics 27, (1978).
|
[21] |
F. L. Mitchell, J. Brady, B. Bextine and I. M. Lauziére, Seasonal increase of Xylella fastidiosa in Hemiptera collected from central Texas vineyards,, J. Econ. Entomol., 102 (2009), 1743.
doi: 10.1603/029.102.0503. |
[22] |
L. Morano, J. Yoon, A. Abedi and F. Mitchell, Evaluation of xylem-feeding insects (Hemiptera: Auchennorrhyncha) in Texas vineyards: distribution along state-wide environmental gradients,, Southwest. Entomol., 35 (2010), 503.
doi: 10.3958/059.035.0402. |
[23] |
R. Redak, et al., The biology of xylem fluid-feeding insect vectors of Xylella fastidiosa and their relation to disease epidemiology,, Annu. Rev. Entomol., 49 (2004), 243.
doi: 10.1146/annurev.ento.49.061802.123403. |
[24] |
S. Ruan, Delay differential equations in single species dynamics,, in Delay Differential Equations and Applications (eds. O. Arino et al.), (2006), 477.
doi: 10.1007/1-4020-3647-7_11. |
[25] |
M. Setamou and W. A. Jones, Biology and biometry of sharpshooter Homalodisca coagulata (Homoptera: Cicadellidae) reared on cowpea,, Ann. Entomol. Soc. Am., 98 (2005), 322. Google Scholar |
[26] |
J. Maynard Smith, Models in Ecology,, Cambridge University Press, (1974). Google Scholar |
[27] |
Hal Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences,, Springer, (2011).
doi: 10.1007/978-1-4419-7646-8. |
[28] |
D. Takiya, S. McKamey and R. Cavichioli, Validity of Homalodisca and of H. vitripennis as the name for glassy-winged sharpshooter (Hemiptera: Cicadellidae),, Ann. Entomol. Soc. Am., 99 (2006), 648. Google Scholar |
[29] |
T. E. Wheldon, Mathematical Models in Cancer Research,, Adam Hilger, (1988). Google Scholar |
[30] |
E. M. Wright, The non-linear difference-differential equation,, Q. J. Math., 17 (1946), 245.
|
show all references
References:
[1] |
R. Almeida, et al., Vector trasmission of Xylella fastidiosa: Applying fundamental knowledge to generate disease management strategies,, Ann. Entomol. Soc. Am., 98 (2005), 775. Google Scholar |
[2] |
M. Begon, J. Harper and C. Townsend, Ecology: Individuals, Populations and Communities,, 2nd edition, (1990). Google Scholar |
[3] |
M. Blua, P. Philips,and R. A. Redak, A new sharpshooter threatens both crops and ornamentals,, Calif. Agr., 53 (1999), 22.
doi: 10.1094/PHP-2000-0627-01-RS. |
[4] |
S. Choi and N. Koo, Oscillation theory for delay and neutral differential equations,, Trends Math., 2 (1999), 170. Google Scholar |
[5] |
D. R. Causton and J. C. Venus, The Biometry of Plant Growth,, Edward Arnold, (1981).
doi: 10.1111/j.1365-3040.1978.tb00759.x. |
[6] |
J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics,, Lecture Notes in Biomathematics 20, (1977).
|
[7] |
J. De Leon, W. Joses and D. Morgan, Population genetic structure of Homalodisca coagulata (Homoptera: Cicadellidae), the vector of the bacterium Xylella fastidiosa causing Pierce's disease in grapevines,, Ann. Entomol. Soc. Am., 97 (2004), 809. Google Scholar |
[8] |
, ., (). Google Scholar |
[9] |
W. W. Fox, An exponential surplus yield model for optimizing in exploited fish populations,, T. Am. Fish. Soc., 99 (1970), 80.
doi: 10.1577/1548-8659(1970)99<80:AESMFO>2.0.CO;2. |
[10] |
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics,, Mathematics and its Applications 74, (1992).
|
[11] |
J. Grandgirard, G. Roderick, N. Davies, M. S. Hoddle and J. N. Petit, Engineering an invasion: Classical biological control of the glassy-winged sharpshooter, Homalodisca vitripennis, by the egg parasitoid Gonatocerus ashmeadi in Tahiti and Moorea, French Polynesia,, Biol. Invasions, 10 (2008), 135.
doi: 10.1007/s10530-007-9116-y. |
[12] |
N. Hayes, Roots of the transcendendal equation associated with a certain differential difference equation,, J. London Math. Soc., 25 (1950), 226.
doi: 10.1112/jlms/s1-25.3.226. |
[13] |
W. Hewitt, The probable home of Pierce's disease virus,, Plant Dis. Rep., 42 (1958), 211. Google Scholar |
[14] |
C. B. Hutchinson, Circular causal systems in ecology,, Ann. N.Y. Acad. Sci., 50 (1948), 221.
doi: 10.1111/j.1749-6632.1948.tb39854.x. |
[15] |
, ., (). Google Scholar |
[16] |
M. Kot, Elements of Mathematical Ecology,, Cambridge University Press, (2001).
doi: 10.1017/CBO9780511608520. |
[17] |
R. Krugner, J. R. Hagler, J. G. Morse, A. P. Flores, R. L. Groves and M. W. Johnson, Seasonal population dynamics of Homalodisca vitripennis (Hemiptera: Cicadellidae) in sweet orange trees maintained under continuous deficit irrigation,, J. Econ. Entomol., 102 (2009), 960.
doi: 10.1603/029.102.0315. |
[18] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics,, Academic Press, (1993).
|
[19] |
I. M. Lauziére, S. Sheather and F. L. Mitchell, Seasonal abundance and spatio-temporal distribution of dominant xylem fluid-feeding Hemiptera in vineyards of central Texas and surrounding habitats,, Environ. Entomol., 37 (2008), 925. Google Scholar |
[20] |
N. MacDonald, Time Lags in Biological Models,, Lecture Notes in Biomathematics 27, (1978).
|
[21] |
F. L. Mitchell, J. Brady, B. Bextine and I. M. Lauziére, Seasonal increase of Xylella fastidiosa in Hemiptera collected from central Texas vineyards,, J. Econ. Entomol., 102 (2009), 1743.
doi: 10.1603/029.102.0503. |
[22] |
L. Morano, J. Yoon, A. Abedi and F. Mitchell, Evaluation of xylem-feeding insects (Hemiptera: Auchennorrhyncha) in Texas vineyards: distribution along state-wide environmental gradients,, Southwest. Entomol., 35 (2010), 503.
doi: 10.3958/059.035.0402. |
[23] |
R. Redak, et al., The biology of xylem fluid-feeding insect vectors of Xylella fastidiosa and their relation to disease epidemiology,, Annu. Rev. Entomol., 49 (2004), 243.
doi: 10.1146/annurev.ento.49.061802.123403. |
[24] |
S. Ruan, Delay differential equations in single species dynamics,, in Delay Differential Equations and Applications (eds. O. Arino et al.), (2006), 477.
doi: 10.1007/1-4020-3647-7_11. |
[25] |
M. Setamou and W. A. Jones, Biology and biometry of sharpshooter Homalodisca coagulata (Homoptera: Cicadellidae) reared on cowpea,, Ann. Entomol. Soc. Am., 98 (2005), 322. Google Scholar |
[26] |
J. Maynard Smith, Models in Ecology,, Cambridge University Press, (1974). Google Scholar |
[27] |
Hal Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences,, Springer, (2011).
doi: 10.1007/978-1-4419-7646-8. |
[28] |
D. Takiya, S. McKamey and R. Cavichioli, Validity of Homalodisca and of H. vitripennis as the name for glassy-winged sharpshooter (Hemiptera: Cicadellidae),, Ann. Entomol. Soc. Am., 99 (2006), 648. Google Scholar |
[29] |
T. E. Wheldon, Mathematical Models in Cancer Research,, Adam Hilger, (1988). Google Scholar |
[30] |
E. M. Wright, The non-linear difference-differential equation,, Q. J. Math., 17 (1946), 245.
|
[1] |
Xin Guo, Lexin Li, Qiang Wu. Modeling interactive components by coordinate kernel polynomial models. Mathematical Foundations of Computing, 2020, 3 (4) : 263-277. doi: 10.3934/mfc.2020010 |
[2] |
Nabahats Dib-Baghdadli, Rabah Labbas, Tewfik Mahdjoub, Ahmed Medeghri. On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021004 |
[3] |
Min Chen, Olivier Goubet, Shenghao Li. Mathematical analysis of bump to bucket problem. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5567-5580. doi: 10.3934/cpaa.2020251 |
[4] |
Philippe G. Ciarlet, Liliana Gratie, Cristinel Mardare. Intrinsic methods in elasticity: a mathematical survey. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 133-164. doi: 10.3934/dcds.2009.23.133 |
[5] |
M. Dambrine, B. Puig, G. Vallet. A mathematical model for marine dinoflagellates blooms. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 615-633. doi: 10.3934/dcdss.2020424 |
[6] |
Chun Liu, Huan Sun. On energetic variational approaches in modeling the nematic liquid crystal flows. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 455-475. doi: 10.3934/dcds.2009.23.455 |
[7] |
Jean-Paul Chehab. Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021002 |
[8] |
Hong Fu, Mingwu Liu, Bo Chen. Supplier's investment in manufacturer's quality improvement with equity holding. Journal of Industrial & Management Optimization, 2021, 17 (2) : 649-668. doi: 10.3934/jimo.2019127 |
[9] |
Skyler Simmons. Stability of broucke's isosceles orbit. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021015 |
[10] |
Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020446 |
[11] |
Urszula Ledzewicz, Heinz Schättler. On the role of pharmacometrics in mathematical models for cancer treatments. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 483-499. doi: 10.3934/dcdsb.2020213 |
[12] |
Jakub Kantner, Michal Beneš. Mathematical model of signal propagation in excitable media. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 935-951. doi: 10.3934/dcdss.2020382 |
[13] |
François Ledrappier. Three problems solved by Sébastien Gouëzel. Journal of Modern Dynamics, 2020, 16: 373-387. doi: 10.3934/jmd.2020015 |
[14] |
Ugo Bessi. Another point of view on Kusuoka's measure. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020404 |
[15] |
Jun Zhou. Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5581-5590. doi: 10.3934/cpaa.2020252 |
[16] |
Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner, Christina Surulescu, Jonas Lenz. Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 443-481. doi: 10.3934/dcdsb.2020284 |
[17] |
Huijuan Song, Bei Hu, Zejia Wang. Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 667-691. doi: 10.3934/dcdsb.2020084 |
[18] |
Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219 |
[19] |
Martin Kalousek, Joshua Kortum, Anja Schlömerkemper. Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 17-39. doi: 10.3934/dcdss.2020331 |
[20] |
Sarra Nouaoura, Radhouane Fekih-Salem, Nahla Abdellatif, Tewfik Sari. Mathematical analysis of a three-tiered food-web in the chemostat. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020369 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]