Delay differential population models for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) densities over a ten-year period
2019 American Control Conference (ACC)
The glassy-winged sharpshooter, Homalodisca vitripennis, is an invasive pest which presents a major economic threat to grape industries in California, as well as Texas  and other wine growing regions, because it spreads a disease-causing bacterium, Xylella fastidiosa. We continue an earlier investigation  into a long-term phenological decline of H. vitripennis densities by studying a system of delayed dierential equations (DDEs) and analyzing aggregate population data for H. vitripennis
... for H. vitripennis from a 10-year study in which bi-weekly monitoring of H. vitripennis populations decreased signicantly. These data present several challenges for modelers. First, they involve truly aggregate population level sampling and hence cannot properly be treated as ordinary longitudinal time series data corresponding to individual level models. The appropriate modeling involves estimation of probability distributions for parameters rather than estimation of the dynamic parameters themselves. Moreover, our analysis reveals that the correct corresponding statistical models involve errors that are observation size dependent (e.g., relative errors should be employed in statistical models). We use these data to test whether DDEs are useful in modeling the observed H. vitripennis population decline. To do this, we perform an analysis of variance (ANOVA) type test comparing the glassy-winged sharpshooter (GWSS) model with delay to the model without delay  . The model is t to the aggregate H. vitripennis data using iterative reweighted weighted least squares (IRWLS) by estimating probability densities over the delay and one of the birthrate parameters. Results indicate that a positive delay provides improvement with a signicance level of p < 0:005.