Mathematical Biosciences and Engineering, 2014, 11(3): 667-677. doi: 10.3934/mbe.2014.11.667

Primary: 92D25, 92D40; Secondary: 93C23.

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Mathematical modeling of Glassy-winged sharpshooter population

1. Department of Mathematics and Statistics, University of Houston - Downtown, Houston, TX 77002
2. Department of Natural Sciences, University of Houston - Downtown, Houston, TX 77002
3. University of Houston - Downtown, Houston, TX 77002
4. Department of Entomology, Texas A&M AgriLife Research, Stephenville, TX 76401

Pierce's disease (PD) is a fatal disease of grapevines whichresults from an infection by the plant pathogen Xyllelafastidiosa. This bacterium grows in the xylem (water-conducting)vessels of the plant blocking movement of water. PD can kill vinesin one year and poses a serious threat to both the California andthe expanding Texas wine industries. Bacteria are vectored fromone vine to the next by a number of xylem feeding insect species.Of these, the Glassy-winged Sharpshooter (GWSS) is considered tobe the primary xylem feeding insect in Texas vineyards. Anextensive database of the xylem-feeding population frequencies wascollected by USDA-APHIS for Texas vineyards over multiple years.This project focused on a subset of data, GWSS frequencies within25 vineyards in Edwards Plateau located in central Texas. Theproposed model investigates the natural population dynamics andthe decline in GWSS, likely the result of pest managementcampaigns on the insects within the region. The model is a delayGompertz differential equation with harvesting and immigrationterms, and we use the data to estimate the model parameters.
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