Research
My primary research interest lies in mathematical biology, where I develop and analyze models of complex systems. Current applications include fluid-based dispersal of organisms and substance use epidemiology. My work generally consists of developing systems of ordinary or partial differential equations, numerically approximating solutions to them, and then using real data to analyze these systems and determine their driving factors. I have also previously created individual-based models. Much of my work is computational and is implemented in Python.
Dispersal of Parasitoid Wasp and their Host
Collaborators:
Dr. Christopher Strickland
Parasitoid wasps are a critical group of insects valued for their use in agricultural biocontrol. As parasitoids, they lay their eggs on or inside host species, eventually killing the hosts parasitized in this way. Since many are highly specialized in the hosts they target, this greatly limits the potential biological side effects inherent in a novel species introduction. However, data collection and modeling efforts related to understanding these insects’ spatial movement remain a significant challenge. Both the wasps and their host are often less than 1 mm in size, and since their flight is primarily wind-based, they can travel for kilometers from their original release point, resulting in a hard, multi-scale challenge. We are building off an existing mathematical model for parasitoid wasp dispersal from a point release, as in the case of biocontrol scenarios, to determine their spatial effect on the target host species. Using a combination of analytic solutions and finite-difference approximations along with half-hourly data collected on wind velocity, we create a coupled, two-dimensional, spatial-temporal model for the dispersal of the parasitoid wasp Eretmocerus hayati and their hosts, the whitefly Bemisia tabaci. We combine both continuous and discrete-time dynamics to tackle this inherently multi-scale problem with the goal of incorporating data from a first-time biocontrol release.
Opioid Epidemic in Veterans and other Vulnerable Subcommunities
Opioid addiction is a national epidemic that has been ongoing for decades. A rise in prescribing opioids in the 1990s led to rises in non-medical heroin and, more recently, fentanyl use. The increased availability of prescription and illicit opioids has led to fatal and nonfatal overdoses throughout the country. In collaboration with Oak Ridge National Lab and Veterans Affairs, we have created a two-part compartmental model for prescription opioid and fentanyl/heroin use disorder and overdoses which aims to better understand how two specific factors affect opioid use in a vulnerable subpopulation: (1) the prevalence of opioid use within the larger community and (2) the availability of resources that specifically target the subcommunity. Mathematical analysis of the model and comparison with population-level data reveal how the subcommunity compares to and is influenced by the community at large. We will use this model to predict the epidemic’s trends and quantify risk factors that will inform patient treatment decisions.
