Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model

In this effort we explain fundamental formulations for aggregate data inverse problems requiring estimation of probability distribution parameters. We use as a motivating example a class of CAR T-call cancer models in mice. After ascertaining results on model stability and sensitivity with respect to parameters, we carry out first elementary computations on the question how much data is needed for successful estimation of probability distributions

Population model for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) over a ten-year period

The glassy-winged sharpshooter, Homalodisca vitripennis (Germar), is an invasive pest which presents a major economic threat to grape industries in California, because it spreads a disease-causing bacterium, Xylella fastidiosa. In this note we develop a time and temperature dependent mathematical model to analyze aggregate population data for H. vitripennis from a 10-year study consisting of biweekly monitoring of H. vitripennis populations on unsprayed citrus, during which H. vitripennis decreased significantly. This model was fitted to the aggregate H. vitripennis time series data using iterative reweighted weighted least squares (IRWLS) with assumed probability distributions for certain parameter values. Results indicate that the H. vitripennis model fits the phenological and temperature data reasonably well, but the observed population decrease may possibly be attributed to factors other than the abiotic effect of temperature. A key factor responsible for this decline but not analyzed here could be biotic, for example, potentially parasitism of H. vitripennis eggs by Cosmocomoidea ashmeadi. A biological control program targeting H. vitripennis utilizing the mymarid egg parasitoid Cosmocomoidea (formerly Gonatocerus) ashmeadi (Girault) is described