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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), 775-786. |
[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), 22-25.
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), 170-176. |
[5] |
D. R. Causton and J. C. Venus, The Biometry of Plant Growth, Edward Arnold, London, 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, Springer-Verlag, 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), 809-818. |
[8] | |
[9] |
W. W. Fox, An exponential surplus yield model for optimizing in exploited fish populations, T. Am. Fish. Soc., 99 (1970), 80-88.
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, 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 glassy-winged sharpshooter, Homalodisca vitripennis, by the egg parasitoid Gonatocerus ashmeadi in Tahiti and Moorea, French Polynesia, Biol. Invasions, 10 (2008), 135-148.
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), 226-232.
doi: 10.1112/jlms/s1-25.3.226. |
[13] |
W. Hewitt, The probable home of Pierce's disease virus, Plant Dis. Rep., 42 (1958), 211-215. |
[14] |
C. B. Hutchinson, Circular causal systems in ecology, Ann. N.Y. Acad. Sci., 50 (1948), 221-246.
doi: 10.1111/j.1749-6632.1948.tb39854.x. |
[15] | |
[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), 960-973.
doi: 10.1603/029.102.0315. |
[18] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 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), 925-937. |
[20] |
N. MacDonald, Time Lags in Biological Models, Lecture Notes in Biomathematics 27, Springer-Verlag, Heidelberg, 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), 1743-1749.
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), 503-512.
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), 243-270.
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.), Springer, Berlin, 2006, 477-517.
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), 322-328. |
[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.
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), 648-655. |
[29] |
T. E. Wheldon, Mathematical Models in Cancer Research, Adam Hilger, Bristol, 1988. |
[30] |
E. M. Wright, The non-linear difference-differential equation, Q. J. Math., 17 (1946), 245-252. |
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), 775-786. |
[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), 22-25.
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), 170-176. |
[5] |
D. R. Causton and J. C. Venus, The Biometry of Plant Growth, Edward Arnold, London, 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, Springer-Verlag, 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), 809-818. |
[8] | |
[9] |
W. W. Fox, An exponential surplus yield model for optimizing in exploited fish populations, T. Am. Fish. Soc., 99 (1970), 80-88.
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, 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 glassy-winged sharpshooter, Homalodisca vitripennis, by the egg parasitoid Gonatocerus ashmeadi in Tahiti and Moorea, French Polynesia, Biol. Invasions, 10 (2008), 135-148.
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), 226-232.
doi: 10.1112/jlms/s1-25.3.226. |
[13] |
W. Hewitt, The probable home of Pierce's disease virus, Plant Dis. Rep., 42 (1958), 211-215. |
[14] |
C. B. Hutchinson, Circular causal systems in ecology, Ann. N.Y. Acad. Sci., 50 (1948), 221-246.
doi: 10.1111/j.1749-6632.1948.tb39854.x. |
[15] | |
[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), 960-973.
doi: 10.1603/029.102.0315. |
[18] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 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), 925-937. |
[20] |
N. MacDonald, Time Lags in Biological Models, Lecture Notes in Biomathematics 27, Springer-Verlag, Heidelberg, 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), 1743-1749.
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), 503-512.
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), 243-270.
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.), Springer, Berlin, 2006, 477-517.
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), 322-328. |
[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.
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), 648-655. |
[29] |
T. E. Wheldon, Mathematical Models in Cancer Research, Adam Hilger, Bristol, 1988. |
[30] |
E. M. Wright, The non-linear difference-differential equation, Q. J. Math., 17 (1946), 245-252. |
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