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Hanakapi'ai Beach Kauai, Hawaii USA
Recent Publications
Recent Publications
In this project, we consider standard epidemic models as a Markov Chain process. We propose a more intuitive method for epidemic analysis through viewing a virus's spread through the ICC (Incidence, Case Count) curve. Statistical analysis shows agreement with traditional compartmental models and offers a time-independent perspective on an epidemics spread. This allows for easier comparison between locations where time-scales of the virus might vary. Numerically, we consider network simulations of these results and ask how does the spread of the disease depend on the network structure.
Collaborators: Joceline Lega, Faryad Sahneh, Joe Watkins
Producing efficient and accurate simulations is crucial to many applications in inverse problems, parameter estimation, engineering and many other fields. Here, we seek to produce a Reduced Order Model through the use of an Autoencoder and Dynamic Identification algorithms with the hopes of retaining accurate simulations in fractions of the time.
We hope that by understanding the dynamics of the latent-space discovered by the autoencoder, we can extend the simulation capabilities of similar parameter regimes by adjusting initial conditions in accordance with parameter adjustments. This would allow high order simulations to be simulated through simple ODE integration techniques and decoded through the trained decoder.
Advisor: Youngsoo Choi (LLNL)
Current Projects
Current Projects
Arizona COVID-19 ICC Curves
Arizona COVID-19 ICC Curves
Previous work shows that an epidemic can be analyzed as a pure-birth Markov Chain by tracking the total number of cases. We investigate the statistical properties of these models and to what extent these mean-field analysis applies. Ultimately, we seek to find the "change point" for accurate understanding of when public policy and or social behaviors have impacted an epidemics trajectory.
Collaborators: Joceline Lega and Joe Watkins
Red: Strong Republican Tie | Blue: Strong Democrat Die
Political Networks and COVID-19 Mitigation
Political Networks and COVID-19 Mitigation
In this project I take a data-driven approach to understanding how state-level politics informed COVID-19 mitigations strategies throughout the course of the pandemic. I consider four separate markers: Governor affiliation, State Legislature majority, State Senate majority, and 2020 Electoral College, and seek to understand which of these best predicts any particular states response to the pandemic.
To approach this problem, I use a combination of statistical testing, machine learning, and inference on the resulting networks to best understand which markers appear to have the most influence on a states particular mitigation strategy and if there are significant differences between states.
Finally, I will analyze this with Google Mobility Data in a hopes of understanding to what effect each of these strategies had and if, again, there is a correlation between the collective behavior and any of the prescribed markers.
Many researchers have proposed various disease-behavior models in an effort to understand the impact of behaviors on disease spreading. These models typically consider one or two behaviors and how their dynamics might impact the spread of a disease. However, researchers often justify the use of these models through heuristic arguments and their ability to fit parameters to real-world data.
We propose a slightly different approach. Instead of measuring behaviors, we use the traditional SIR model and allow for two variations to capture all behavior dynamics: a dynamic population size and dynamic disease parameters. Many of the existing disease-behavior models can be categorized in this fashion, hinting at the universality of such a model. Finally, we hope to use this model to analyze real-world data to make more accurate predictions based on various behavior indicators such as social media, surveys, and sociological research.
Advisor: Joceline Lega
Past Projects
Past Projects
With the large influx of data in recent decades, we try to develop resources to help understand the underlying dynamics to certain data sets. Nathan Kutz and his collaborators developed the Sparse Identification of Nonlinear Dynamics (SINDy) at the University of Washington. Our goal is to use this tool in conjunction local dynamical data to ulitmately find governing PDEs to various physical, biological and social systems.
Advisor: Joceline Lega
In this paper, we explore "The Hidden Geometry of Complex, Network-Driven Contagion Phenomena'' by Brockman and Helbing and its contribution to the mathematics of large-scale epidemic modeling. Given a network that describes the cities around the world, Brockman and Helbing consider how diseases might spread if the distance between cities is based on the transportation between them instead of the geographic distance. We then consider the effects of down-scaling the model to a country-level and analyze how reasonable this might be. specifically with COVID-19 and US air travel.
Advisor: Joceline Lega
Dynamics and Energy analysis of bistable shallow arches
Dynamics and Energy analysis of bistable shallow arches
Consider a thin ribbon of metal with is constructed to have a slight bend. This bend can be in either direction (up or down). We can link arches in such a way that when we push one, it forces those linked to it to might switch as well. We look to analyze linked arches, their dynamics, energy needed to flip multiple arches. We also consider when we have a closed loop (triangle, square, pentagon, etc.) and how this might effect the dynamics.
Advisor: Eleanora Tubaldi
In this paper we explore the introductory theory of modeling epidemics on networks and the significance of the spectral radius in their analysis. We look to establish properties of the spectral radius that would better inform how an epidemic might spread over such a network. We construct a specific transformation of networks that describe a transition from a star network to a path network. For the sequence of adjacency matrices that describe the unfolding of a star into a path, we show the spectral radius of these graphs can be given in a simple algebraic equation. Using this equation we show the spectral radius increases as the star unfolds and establish bounds on the spectral radius for each network.
Advisor: Miaohua Jiang
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