Ryan Weightman, Ph.D.

Optimized COVID Vaccination Plan

2022-03-17T00:00:00-05:00

The COVID-19 outbreak gave rise to an unprecedented production of models and studies aimed at understanding the pandemic, predicting its evolution and designing measures to reduce its spread. There was an especially strong focus on how to accurately model vaccination of a certain population in a compartmental SIR model. We build a SIR model with vaccination compartments and exposed compartment transforming it into an SVEIR model. We then split the population into major age groups to better capture the varying effect of the virus on specific populations. Lastly, we optimize vaccine schedule to minimize deaths amongst the population. All of this is done in Python using an optimation package. View our research here.

Modeling the Control of COVID via Non-Pharmaceutical Intervention

2021-10-08T00:00:00-05:00

The COVID-19 outbreak gave rise to an unprecedented production of models and studies aimed at understanding the pandemic, predicting its evolution and designing measures to reduce its spread.The aim of this project is to show how a simple SIR model was used to make quick predictions for New Jersey in early March 2020 and call for action based on data from China and Italy. Now different viruses manifest with different characteristics and public response to these characteristics can be drastically different. Therefore A more refined model, which accounts for the parameters social distancing, testing, contact tracing and quarantining, is then proposed to identify containment measures to minimize the economic cost of the pandemic.

This model was programmed using AMPL (a mathematical programming language) in which we use optimization techniques and data from throughout New Jersey, split into three regions, to minimize the economic costs of the aforementioned parameters. For visualization and plotting we use Matlab to plot our results. Our paper can be found here

Steiner symmetrization and the eigenvalues of the Laplace operator on polygons

2021-05-05T00:00:00-05:00

The topic that I chose to explore for my Master's Thesis is a study of the eigenvalues of the Dirichlet Laplacian on a two dimensional domain and the properties that arise as a direct consequence to them. The eigenvalues of a given domain produce so many surprising insights that simply the study of a triangular domain kept me busy throughout my project! What I love about this topic is that throughout my study, a resource from 1966 could take me to a resource from the 1700’s which could lead me all the way back to 2013. It is a topic rich with exploration, both new and old which really gave me a good picture of what modern research in pure mathematics can look like. To view this thesis, follow this link .