Student Poster Presentations

COLLOQUIUM
Thursday, January 27, 11 :00AM
In Person Event: 121 Manchester Hall

Student Poster Presentations

Since the Joint Math Meetings were canceled, the Department of Mathematics and Statistics has decided to host a mini poster session for our students as well as their Elon colleagues. Students and faculty are warmly welcomed to attend.

The titles and abstracts of the posters are below.

Optimal Intervention Strategies to Minimize Spread of Infectious Diseases and Economic Impact.

Students: Danielle DaSilva, Minato Hiraoka, Malindi Whyte

Abstract: We investigate the economic impacts of pharmaceutical and non-pharmaceutical
interventions on the labor force during an epidemic. Specifically, we study an optimal control
problem on a dynamic SIV-type small-world network model with controls corresponding to
vaccinations and other intervention strategies. The cost functional utilized is a Cobb-Douglas
production function measuring labor productivity as well as a functional measuring the cost of
treating the disease. We numerically approximate the economic impact enforcing this control
strategy which allows us to determine the optimal vaccination policy. These methods illustrate
the usefulness of this approach to inform policymakers and better equip society for emerging
epidemics.

Finite Time Blowup for the Nonlinear Schrodinger Equation with a Delta Potential

Student: Eoghan O’Keefe

Abstract: In this presentation, we study the Cauchy problem for the nonlinear Schrodinger
equation with a delta potential. We show that under certain conditions, the sup norm of the
solution tends to infinity in finite time. In order to prove this, we study the associated
Lagrangian and Hamiltonian, and derive an estimate of the associated variance. We also
derive several conservation laws which a classical solution of the Cauchy problem must also
satisfy.

Using a Network Model to Control the Spread of an Infectious Disease on a College Campus with Contact Tracing

Students: Christopher Boyette, Sarah Ruth Nichols

Abstract: The control of infectious diseases has been a topic of recent discussion due to the
emergence of COVID-19. To study this issue, we use an SIR-type model on a dynamic
network to analyze the effect of contact tracing, quarantining, and asymptomatic testing on
disease spread. Our model emulates a college campus environment with a special emphasis
on interactions between cliques, mirroring the dormitory and extracurricular environment.
This study mimics the measures that were utilized by our own campuses to contain the
transmission of the virus in a close living situation. We also examine different types of
mandatory COVID-19 testing and identify which are the most efficient at determining the
accurate number of infected individuals. Lastly, we analyze our findings using Monte Carlo
simulations to determine effectiveness of different control measures in a randomized setting.

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