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  Epidemic dynamics on networks

  
  

  In the 2015 REU on Dynamics and Stochastics at Brown University, I co-mentored two students who studied the impact of human interactions through home, social, and work/school contexts on the spread of influenza. We extended diary-based network data to larger networks of human interaction and identified strategies that may lead to more effective suppression of disease spread on these realistic networks.

  Students: Joshua Rubin Abrams (University of Arizona), Anne Schwartz (Connecticut College), Kristina Mallory (Brown University)
  Other collaborators: Alexandria Volkening (Northwestern University), Björn Sandstede (Brown University).
  Preprints:

  1. JR Abrams, A Schwartz, MV Ciocanel, K Mallory, A Volkening, and B Sandstede. Influenza spread on context-specific networks lifted from interaction-based diary data (Submitted, 2020).

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  Stability of agent-based models for zebrafish stripe formation

  
  

  In the Summer @ ICERM 2016 REU program, I co-mentored three students in studying the stability of patterns arising in agent-based models, motivated by zebrafish stripe formation. We used the framework of piecewise-deterministic Markov processes (PDMPs) to account for deterministic and stochastic processes occurring on the same timescale in these models.
  Students: Cassandra Cole (Brown University), Philip Doldo (RPI), Qing Fan (Pomona College).
  Other collaborators: Alexandria Volkening (MBI, OSU), Björn Sandstede (Brown University).
  Student awards:
  

  1. Claire, Cassie and Philip won an Outstanding Poster Award in the Applied Mathematics category at the JMM Undergraduate Poster Session in January 2017!

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  Lead propagation in the body

  
  

  In the Summer @ ICERM 2016 REU program, I co-mentored two students studying lead accumulation in the body after decades from ingestion. We developed ODE and PDE models and investigated the impact of nonlinearities and diffusion in modeling lead propagation.

  Students: Jordan Collignon (California State University, Monterey Bay), Melissa Morrissey (Brown University).
  Other collaborators: Todd Kapitula (Calvin College).
  Student publication:
  

  1. M Morrissey, J Collignon. Propagation of lead in the human body. SIURO (10) 2017 PDF.

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  Topological data analysis for cellular rings

  
  

  In the summer of 2018, I mentored a student from Tulane University studying novel topological data analysis methods and visualization for intracellular transport. In particular, we developed methods and algorithms to identify significant ring openings using Betti 1 numbers for time-series simulation and experimental data.

  Students: Riley Juenemann (Tulane University).
  Other collaborators: Adriana Dawes (OSU), Scott McKinley (Tulane University).
  Preprints:
  

  1. MV Ciocanel, R. Juenemann, A Dawes, S McKinley. Topological data analysis approaches to uncovering the timing of ring structure onset in filamentous networks (In revision). arXiv preprint .

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