Spatial epidemiology project
Research in this project is focused on the following topics (in no particular order):
- What is the best discrete-time discrete-space form of the reaction-diffusion equations for modeling real-world epidemics?
- In the Hoppenstaedt version of the spatial epidemic, should the kernel function be scale-free?
- How can we best incorporate mass movements of populations as they flee a major epidemic?
- Which versions of the Ensemble Kalman Filter (EnKF) work the best for tracking epidemics?
- Might a particle filter operated by a genetic algorithm perform better than an ensemble filter?
- In any filter used for tracking purposes, should we apply the filter to a transformed state space?
- How can we best model transportation networks?
- How can we best estimate the epidemic's parameters?
Overall leadership of this project lies with Dr. Loren Cobb, of the Department of Mathematical and Statistical Sciences.
- The spatial epidemiology project of the Center for Computational Mathematics was funded by a two-year Challenge Grant from the National Library of Medicine from October 2009 to September 2011.
- Jan Mandel, Loren Cobb, and Jonathan D. Beezley, On the Convergence of the Ensemble Kalman Filter, CCM Report 278, January 2009. arXiv:0901.2951 Accepted in Applications of Mathematics
Conference proceedings and book chapters
- Jan Mandel, Jonathan D. Beezley, Loren Cobb, and Ashok Krishnamurthy, "Data Driven Computing by the Morphing Fast Fourier Transform Ensemble Kalman Filter in Epidemic Spread Simulations", Procedia Computer Science, vol 1, 1215–23, May 2010. arXiv:1003.1771 CCM Report 285 paper UCD
- Ashok Krishnamurthy, Loren Cobb, Jan Mandel, and Jonathan D. Beezley, Bayesian Tracking of Emerging Epidemics Using Optimal Statistical Interpolation, 2010 Joint Statistical Meetings, Vancouver, Canada, July 31- August 5, 2010, pp. 3471-3485. arXiv:1009.4959pdf abstract
- Jonathan D. Beezley, Jan Mandel, and Loren Cobb, Wavelet Ensemble Kalman Filters, Proceedings of the 6th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS'2011), Prague, September 15--17, 2011, 514--518, 2011, ISBN 978-1-4577-1423-8. arXiv:1102.5554
- Jan Mandel, Jonathan D. Beezley, and Loren Cobb, Spectral and morphing ensemble Kalman filters, AMS 91st Annual Meeting, Seattle, WA, 23-27 January 2011, paper J12.7. abstract paper pdf paper sources presentation pdf presentation files
- Jan Mandel (with J. D. Beezley, L. Cobb, A. Krishnamurthy, A. K. Kochanski, K. Eben, P. Jurus, and J. Resler), Spectral and morphing ensemble Kalman filters and applications, 31st Annual International Symposium on Forecasting, The University of Economics, Prague, June 2011.