My
primary interests are mathematical models in biology and delay differential
equations. Below is a list of some problems on which I am working. (Last
updated Mar. 6, 2023.)
Modeling Cellular Control Systems
One of the important questions, which scientists are currently investigating, concerns how the cell cycle begins in bacterial cells. I have been using information that is known about the biochemical processes in Escherichia coli to try to determine the key controlling steps in the initiation of DNA replication. My studies have examined several aspects of growing cultures of bacterial cells using biochemical kinetics to study cellular control problems from a theoretical perspective. It is hoped that my studies will assist the experimental studies in discovering the most significant steps initiating the cell cycle.
Age-Structured Models for Erythropoiesis
My studies of cellular control systems included some studies on how the process of diffusion can result in effects that are similar to delays in simpler systems of differential equations. My study of age-structured models for erythropoiesis began as an inquiry into the relation between complicated age-structured models to the significantly simpler systems of delay differential equations. In collaboration with Jacques Bélair and Mike Mackey, I have studied some models for hematopoiesis, which have interesting results for both studying hematopoietic diseases and the mathematical study of state-dependent delay differential equations. Recent work has shown how the variable velocity of aging in erythropoiesis can stabilize the mathematical model. Modeling
Marine Phage
Marine bacteriophage play a vital role in the ecology of the oceans, cycling about 25% of the carbon daily. However, little is known about this very important community. I am collaborating with a number of biologists and mathematicians at SDSU to learn more about the diversity and population dynamics of this community. Molecular mechanisms are being modeled to better understand the lytic and lysogenic lifestyles of phage. Also, new models are being developed to help understand the role of diversity and heterogeneity for phage in the marine environment. Modeling efforts have helped narrow the number of "species" of phage in a temperate marine environment and have shown that rank-abundance curves these "species" follow a power law distribution. Experiments are being designed to determine key kinetic parameters to better understand the dynamics of phage and their hosts.
