Mathematical modeling of Glassywinged sharpshooter population
Pages: 667  677,
Issue 3,
June
2014
doi:10.3934/mbe.2014.11.667 Abstract
References
Full text (543.8K)
Related Articles
JeongMi Yoon  Department of Mathematics and Statistics, University of Houston  Downtown, Houston, TX 77002, United States (email)
Volodymyr Hrynkiv  Department of Mathematics and Statistics, University of Houston  Downtown, Houston, TX 77002, United States (email)
Lisa Morano  Department of Natural Sciences, University of Houston  Downtown, Houston, TX 77002, United States (email)
Anh Tuan Nguyen  University of Houston  Downtown, Houston, TX 77002, United States (email)
Sara Wilder  University of Houston  Downtown, Houston, TX 77002, United States (email)
Forrest Mitchell  Department of Entomology, Texas A&M AgriLife Research, Stephenville, TX 76401, United States (email)
1 
R. Almeida, et al., Vector trasmission of Xylella fastidiosa: Applying fundamental knowledge to generate disease management strategies, Ann. Entomol. Soc. Am., 98 (2005), 775786. 

2 
M. Begon, J. Harper and C. Townsend, Ecology: Individuals, Populations and Communities, 2nd edition, Blackwell Scientific Publications, Boston, MA, 1990. 

3 
M. Blua, P. Philips,and R. A. Redak, A new sharpshooter threatens both crops and ornamentals, Calif. Agr., 53 (1999), 2225. 

4 
S. Choi and N. Koo, Oscillation theory for delay and neutral differential equations, Trends Math., 2 (1999), 170176. 

5 
D. R. Causton and J. C. Venus, The Biometry of Plant Growth, Edward Arnold, London, 1981. 

6 
J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics 20, SpringerVerlag, Heidelberg, 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), 809818. 

8 
http://www.epa.gov. 

9 
W. W. Fox, An exponential surplus yield model for optimizing in exploited fish populations, T. Am. Fish. Soc., 99 (1970), 8088. 

10 
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Mathematics and its Applications 74, Kluwer Academic Publishers, Dordrecht, 1992. 

11 
J. Grandgirard, G. Roderick, N. Davies, M. S. Hoddle and J. N. Petit, Engineering an invasion: Classical biological control of the glassywinged sharpshooter, Homalodisca vitripennis, by the egg parasitoid Gonatocerus ashmeadi in Tahiti and Moorea, French Polynesia, Biol. Invasions, 10 (2008), 135148. 

12 
N. Hayes, Roots of the transcendendal equation associated with a certain differential difference equation, J. London Math. Soc., 25 (1950), 226232. 

13 
W. Hewitt, The probable home of Pierce's disease virus, Plant Dis. Rep., 42 (1958), 211215. 

14 
C. B. Hutchinson, Circular causal systems in ecology, Ann. N.Y. Acad. Sci., 50 (1948), 221246. 

15 
http://www.ipm.ucdavis.edu. 

16 
M. Kot, Elements of Mathematical Ecology, Cambridge University Press, 2001. 

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), 960973. 

18 
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993. 

19 
I. M. LauziĆ©re, S. Sheather and F. L. Mitchell, Seasonal abundance and spatiotemporal distribution of dominant xylem fluidfeeding Hemiptera in vineyards of central Texas and surrounding habitats, Environ. Entomol., 37 (2008), 925937. 

20 
N. MacDonald, Time Lags in Biological Models, Lecture Notes in Biomathematics 27, SpringerVerlag, Heidelberg, 1978. 

21 
F. L. Mitchell, J. Brady, B. Bextine and I. M. LauziĆ©re, Seasonal increase of Xylella fastidiosa in Hemiptera collected from central Texas vineyards, J. Econ. Entomol., 102 (2009), 17431749. 

22 
L. Morano, J. Yoon, A. Abedi and F. Mitchell, Evaluation of xylemfeeding insects (Hemiptera: Auchennorrhyncha) in Texas vineyards: distribution along statewide environmental gradients, Southwest. Entomol., 35 (2010), 503512. 

23 
R. Redak, et al., The biology of xylem fluidfeeding insect vectors of Xylella fastidiosa and their relation to disease epidemiology, Annu. Rev. Entomol., 49 (2004), 243270. 

24 
S. Ruan, Delay differential equations in single species dynamics, in Delay Differential Equations and Applications (eds. O. Arino et al.), Springer, Berlin, 2006, 477517. 

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), 322328. 

26 
J. Maynard Smith, Models in Ecology, Cambridge University Press, 1974. 

27 
Hal Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Springer, 2011. 

28 
D. Takiya, S. McKamey and R. Cavichioli, Validity of Homalodisca and of H. vitripennis as the name for glassywinged sharpshooter (Hemiptera: Cicadellidae), Ann. Entomol. Soc. Am., 99 (2006), 648655. 

29 
T. E. Wheldon, Mathematical Models in Cancer Research, Adam Hilger, Bristol, 1988. 

30 
E. M. Wright, The nonlinear differencedifferential equation, Q. J. Math., 17 (1946), 245252. 

Go to top
