This project considered a system of linear ODEs to model the degradation of a peptide substrate reporter for protein kinase B (VI-B) in five different cell cultures from data provided by the Chemistry department. After solving these equations one by one, we find the best fit parameters that match the data using least squares tools in Matlab with an iterative approach. Drawing from the histogram plots of parameter distributions, we conclude that the most popular values which yield the smallest residuals are best fit parameters. The figure shows the best fit of our model to the given data. A poster detailing the full problem is here. The paper can be found here.
Variability of Risk in Host-Parsitoid Models
Using the traditional discrete structure of host-parasitoid models, we assume that the parasitoid has a different attack rate for each host, which means each host has variable risk. The risk, x, is assumed to be independent of local host density and distributed according to the continuous probability distribution, p(x). We implement the variability in existing host-parasitoid models to search for the conditions of coexistence of the host larvae population and two parasitoid population, which have different time frames of attack and different rates of attack. The figure shows a stable trajectory in which all three populations coexist. An investigation of the stability region for coexistence is still underway. A poster detailing the model is here.
Host-Parasitoid Semi-Discrete Model with Parasitoid Migration
Using the semi-discrete framework, we investigate the migration of parasitoids between two locations. Typically, hosts are immobile and parasitoids can fly. This figure shows the surface of the third, most restrictive Jury condition for evaluating the stability region in (alpha, beta) space, where alpha and beta are the proportions of host and parasitoids at one location, respectively. The surface lies above the zero plane, indicating that the model is stable for all values of alpha and beta. However, we can see that for some values of alpha and beta, the surface nearly touches the zero plane, which means the system is `less stable' for those values.