I am an applied mathematician with a strong interest in spatial ecology. My primary research focus is on understanding the consequences of dispersal on biological populations under the effects of habitat fragmentation. With my collaborators, I construct mathematical models, explore their distinctive features through mathematical analysis using nonlinear analysis and computational tools, and parameterize these models with data from empirical experiments to study the spatial-temporal dynamics of biological populations.
This collaborative NSF-funded project involves an ecologist at Louisiana State University and a mathematician at University of North Carolina at Greensboro and explores the effects of habitat fragmentation, conditional dispersal, and interspecific interactions on population dynamics from the patch to the landscape level.
This project is a collaboration with entomologists at Mississippi State University which applies mathematical modeling to better understand dispersal of medically important arthopods such as bed bugs and ticks.
An ongoing project that explores the dynamics of reaction diffusion equations arising from models in population dynamics and combustion theory. The main emphasis in this project is the development of new methods in nonlinear analysis to address complexities in the differential equations. Semipostione and positone reaction terms are both included.
The journal article, "Modeling the effects of trait-mediated dispersal on coexistence of mutualists," is published in Mathematical Biosciences and Engineering.
The journal article, "Frequency of Occurrence and Population-Dynamic Consequences of Different Forms of Density- Dependent Emigration," is published in the American Naturalist.
