My research focuses on the development of mathematical models and numerical methods for biological systems. Current projects include:

  1. Interactions between molecular species in cells and tissue (coupled PDEs and stochastic models),
  2. Predicting the movement of locust nymphs (agent-based and PDE models),
  3. Exploring the impact of parasites on interactions of individuals in social groups (ODE and dynamic network models), and
  4. Modeling pattern formations during cell motility (ODE and PDE models).

Interactions between chemical species

Messenger RNA (mRNA) transports genetic information from the nucleus where the DNA is housed to the cytoplasm of the cell where the mRNAs are translated into proteins. In addition to mRNA, we have small, non-coding microRNAs (miRNA) that do not code for proteins like mRNA, but do effect the proteins that become translated. Some of these mRNA and miRNA bindings effect major cell processes such as cell growth, tissue differentiation, or programed cell death. Over-expression of cell growth or under-expression of cell death results in cell overgrowth --- a characteristic of cancer. Modeling the interaction of two (or more) chemical species, specifically focusing on the interactions between mRNA and miRNA, attempts to give insight into our understanding of how mRNA and miRNA molecules interact at the tissue level and the effects of this interaction on gene regulation.

Locust movement

Australian plague locusts are social insects that tend to begin in a solitary, asocial state; however, when solitary locusts congregate together, they transition into a gregarious state where they tend to march together and forage for food in large numbers. What is interesting is that the locust density appears to show a pulse like behavior. Because locusts are so destructive, knowing more about locust band movements may help curtail their speed and spread.

Disease impacts on social groups

Social interactions between individuals in a group may change based on certain influences such as the introduction of a communicable disease or parasite. In particular, I focus on how ectoparasites, those parasites that live on the outside of the host like fleas, may spread via social group interactions and how that impacts the group's social structure and evolutionary success.

Cell motility

As certain types of cells move around or crawl, patterns emerge along the cell’s wall. Although some have researched how the cumulation of molecules create a clustering phenomena on the cell wall, no clear understanding has been made about the development of pattern formation. A particular cell called a keratocyte which is jellybean-like in appearance shows this patterning phenomena. The goal here is to create a model of keratocyte movement to investigate pattern formation on the cell walls of keratocytes.


In print


In preparation

Active research


My thesis research was supported by the San Diego Fellowship, Center for Theoretical Biological Physics (CTBP), National Institues of Health (NIH), and National Science Foundation (NSF).