What would happen if two people out in space a few meters apart, abandoned by their spacecraft, decided to wait until gravity pulled them together? My initial thought was that …
Describe dynamical systems in terms of the differential equations without having to write the coding loops or functions. Easily plot the changes in the variables, show phase plots, and vector fields. Explore examples from modeling the zombie apocalypse, the infectiousness of ideas on Twitter, or the exchange of energy in the Earth climate system. Useful for teaching dynamical systems for students with little programming experience.
Included is an interface to Bayesian MCMC with the emcee package for doing Bayesian parameter estimation and model comparison!
Blais, B.S. and Skaza, J., Modeling the Infectiousness of Twitter Hashtags. Sep 2016. Bryant University Science Seminar.
Skaza, J. and Blais, B.S., Mathematical Modeling of Trending Topics on Twitter. Apr 14, 2015. Honors Capstone Presentation.
Brian Blais, Colin Gannon, Qin Leng, Robert Patalano, Hong Yang. October 2013. Bayesian Parameter Estimation in a 1D Model of Precipitation and Evaporation: Comparison of Middle Miocene and Modern Climates Using Plant Lipid Deuterium dD Measurements Geological Society of America Conference. Some extra slides that didn't fit on the poster.
Modeling Ecosystems and Climates: A Teaching Simulator for Systems Dynamics* (Rhode Island Space Grant Consortium Annual Symposium, November 2009)
Skaza, J. and Blais, B.S. 2015. Modeling the Infectiousness of Twitter Hashtags. Physica A: Statistical Mechanics and its Applications. Volume 465, 1 January 2017, Pages 289–296.
Witkowski, C. and Blais, B.S. 2013. Bayesian analysis of epidemics - zombies, influenza, and other diseases . Available from the arXiv at http://arxiv.org/abs/1311.6376 as well as on ScienceOpen. An iPython notebook with the simulations is available here.
Mathematical models of epidemic dynamics offer significant insight into predicting and controlling infectious diseases. The dynamics of a disease model generally follow a susceptible, infected, and recovered (SIR) model, with some standard modifications. In this paper, we extend the work of Munz et.al (2009) on the application of disease dynamics to the so-called ``zombie apocalypse'', and then apply the identical methods to influenza dynamics. Unlike Munz et.al (2009), we include data taken from specific depictions of zombies in popular culture films and apply Markov Chain Monte Carlo (MCMC) methods on improved dynamical representations of the system. To demonstrate the usefulness of this approach, beyond the entertaining example, we apply the identical methodology to Google Trend data on influenza to establish infection and recovery rates. Finally, we discuss the use of the methods to explore hypothetical intervention policies regarding disease outbreaks.