Mathematical modeling of Glassy-winged sharpshooter population

Pierce's disease (PD) is a fatal disease of grapevines which results from an infection by the plant pathogen Xyllela fastidiosa. This bacterium grows in the xylem (water-conducting) vessels of the plant blocking movement of water. PD can kill vines in one year and poses a serious threat to both the California and the expanding Texas wine industries. Bacteria are vectored from one vine to the next by a number of xylem feeding insect species. Of these, the Glassy-winged Sharpshooter (GWSS) is considered to be the primary xylem feeding insect in Texas vineyards. An extensive database of the xylem-feeding population frequencies was collected by USDA-APHIS for Texas vineyards over multiple years. This project focused on a subset of data, GWSS frequencies within 25 vineyards in Edwards Plateau located in central Texas. The proposed model investigates the natural population dynamics and the decline in GWSS, likely the result of pest management campaigns on the insects within the region. The model is a delay Gompertz differential equation with harvesting and immigration terms, and we use the data to estimate the model parameters.