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RESEARCH

Much of my research takes an interdisciplinary approach to collaboration, where I use mathematical, statistical, and computational methods to answer epidemiological questions about non-infectious diseases.

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I am keenly interested in the structural differences between models of infectious disease and those of substance use disorders, and how they give rise to the need for new mathematical analyses.  My dissertation is primarily focused on how substance abuse and subsequent addiction develops in a population, and how mathematics can shed light on the nuances of these diseases.

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Outside of substance use epidemiology, I developed a Bayesian statistics model through an internship with the UNC School of Medicine to determine if the data suggests there is a central peak time at which sudden death is more likely to occur. Such information can be important to medical providers and EMS who provide potentially life-saving care and resources to victims of sudden death events.

SIR.png

Compartmental diagrams for the classic SIR infectious disease model a general SUD model I created and analyzed using optimal control.  Both models assume that each class represents a proportion of the total population (N=1) and increased death due to infection or addiction.  The SIR model assumes immunity from reinfection while the SUR model allows for relapse.  Most notably, the SUR model allows for SUD to develop without social contact/influence through the pathway ɛS.  This linear perturbation away from SIR causes drastic changes in dynamics, shown below.

Numerical depictions of the dynamical shift caused by the addition of the linear addiction rate ɛS into an SIR-like framework.  Note, when ɛ = 0, there exists both a use disorder-free equilibrium (UDFE) and an endemic equilibrium that change stability at the bifurcation point, namely R_0 = 1 where R_0 is the basic reproductive number.  When this model is perturbed by letting ɛ > 0, the bifurcation point no longer exists and the model produces only one feasible equilibrium that is strictly positive and globally (asymptotically) stable.

Results of the Bayesian statistics model I developed predicting the time of death due to sudden cardiac events.  These images can be thought of as 24-hour clocks showing at what time of day most fatal cardiac events occur given different associated risk factors.  The data used in the creation of these models was relatively small, so the integer C represents a confidence level in the time of death data recorded; the above clocks were produced using only the data we are most confident in recorded time of death (C=1).  The dashed lines embedded on the clocks mark the 90% credible interval. Our model best predicts that those with heart failure are most likely to experience sudden cardiac events in the morning between 4:30am and about 10am.

tau_clocks_C1.png
SUS_bifurcation_plots.png

Upcoming Publications

  • Queen*, Pearcy*, Jodoin, Lenhart, Strickland.  Agent-based dynamics of a SPAHR opioid model on social network structures.  In preparation. (* indicates shared first authorship)

  • Siddiqui, Elzinga, Pearcy, James, Keen, Williams, Simpson.  A Bayesian Analysis of Circadian Variation in Sudden Death in Wake County, North Carolina.  In preparation.

Publications

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