Research Overview
Brief Summaries of Current Research:
Predator-Prey-Parasite Dynamics
I consider a three dimensional ODE system consisting of a predator, prey, and a parasite that infects the prey only, with goals including finding conditions for persistence of each species.
s-bifurcation--high-b.mp4Ecological systems with Darwinian Evolution
I explore under what conditions an organism would evolve, via Darwinian principals, to be semelparous (a single large and life ending reproductive event) or iteroparous (multiple smaller but survivable reproductive events).
Other projects include expanding the existing theory to consider disease dynamics, from both a host perspective (e.g. gaining immunity) and the disease (e.g. a parasite forming a life cycle with multiple hosts).
Epidemics on a Network and Connections with Difference Equations
I aim to connect the day to day data reported on real-world epidemics, which by their nature are on a network, to difference equations. The main aim is to use the difference equation to provide a computationally easy estimate of the associated network parameters.
Mathematics Education
Post COVID teaching has been a challenge for students and teachers. I collaborated with other postdocs and instructors to survey students to determine how to improve emergency transitions in the future, as well as improve on current teaching methods.
Within Host Influenza Dynamics
I focus on recent discoveries in influenza, including semi-infectious particles and defective interfering particles, to update ODE models of within host viral infections. With the updated models