Dr. Lora Billings, Dean |

**Research:**

My research program focuses on applied deterministic and stochastic dynamical systems. By studying the models arising in applications from epidemiology, physics, and ecology, I work towards making significant advances in mathematics as well as impacting the applications. I incorporate students in my research at both the undergraduate and graduate levels.

**Publications:**- Lora Billings and Eric Forgoston, "Seasonal Forcing in Stochastic Epidemiology Models." Richerche di Matematica, 67, 1 (2018) 27-47.
- Pralhad Burli, Eric Forgoston, Pankaj Lal, Lora Billings, and Bernabas Wolde, "Adoption of switchgrass cultivation for biofuel under uncertainty: A discrete-time modeling approach." Biomass and Bioenergy, 105 (2017) 107-115. link
- Garrett T. Nieddu, Lora Billings, James H. Kaufman, Eric Forgoston, and Simone Bianco, "Extinction Pathways and Outbreak Vulnerability in a Stochastic Ebola Model." Journal of The Royal Society Interface 14 (2017). Link
- Martha Bauver, Eric Forgoston, and Lora Billings, "Computing the optimal path in stochastic dynamical systems." Chaos 26, 083101 (2016).
- Jennifer Adams Krumins, Valdis Krumins, Eric Forgoston, Lora Billings and Wim H. van der Putten, "Herbivore efficiency and stoichiometric feedbacks to primary production," PLOS ONE 10 (2015) e0129775. Open Access Article
- Ira B. Schwartz, Lora Billings, Thomas W. Carr, and Mark Dykman, "Noise Induced Switching and Extinction in Systems with Delay," Physical Review E 91, 012139 (2015). PDF
- Garrett Nieddu, Lora Billings, and Eric Forgoston, "Analysis and control of pre-extinction dynamics in stochastic populations," Bulletin of Mathematical Biology 76, 12 (2014) 3122-3137. PDF
- Lora Billings, Luis Mier-y-Teran-Romero, Brandon Lindley, Ira B. Schwartz , "Intervention-Based Stochastic Disease Eradication," PLOS ONE 8 (2013) e70211. Open Access Article
- Lora Billings, "Succeeding in Undergraduate Student Research: A Few Helpful Hints for Advisors," PRIMUS 23,9 (2013) 798-804.
- Jackson Burton, Lora Billings, Derek A. T. Cummings, and Ira B. Schwartz, "Disease Persistence in Epidemiological Models: The Interplay between Vaccination and Migration," Mathematical Biosciences 239, 1 (2012) 91-96. PDF
- Ira B. Schwartz, Thomas W. Carr, Lora Billings, and Mark Dykman, "Noise Induced Switching in Delayed Systems," Naval Research Laboratory Memo Report NRL/MR/6790--129406 (2012). Link
- Eric Forgoston, Lora Billings, Philip Yecko, and Ira B. Schwartz, "Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant," CHAOS 21(1), 013116 (2011). PDF
- Lucas Shaw, William M. Spears, Lora Billings, and Paul M. Maxim, "Effective Vaccination Policies," Information Sciences 180, 19 (2010), 3728-3744. PDF
- Jonathan Ballone (advisor Lora Billings), "Early die out events in SIR epidemic models," Rose Hulman Undergraduate Math Journal, Vol. 11, Issue 1 (2010). Link
- Lora Billings, Mark I. Dykman, Marie McCrary, A. N. Korotkov, and Ira B. Schwartz, "Switching barrier scaling near bifurcation points for non-Gaussian noise," Physical Review Letters 104(14), 140601 (2010). PDF
- Eric Forgoston, Lora Billings, and Ira B. Schwartz, "Accurate Time Series Prediction in Reduced Stochastic Epidemic Models," Chaos 19, 043110 (2009). Abstract, PDF
- Diana Thomas, Marion Weedermann, Lora Billings, Joan Hoffacker, Robert Washington-Allen, "When to Spray: A Time Scale Calculus Approach to Controlling the Impact of West Nile Virus," Ecology and Society 14 (2009) article no. 21. Abstract
- Ira B. Schwartz, Lora Billings, Mark I. Dykman, and Alexandra Landsman, "Predicting extinction rates in stochastic epidemic models" Journal of Statistical Mechanics: Theory and Experiment (2009) P01005. PDF
- Lora Billings, Ira B. Schwartz, and Mark I. Dykman, "Thermally activated switching in the presence of non-Gaussian noise," Physical Review E 78 (2008) 051122. PDF
- Lora Billings and Ira B. Schwartz, "Identifying almost invariant sets in stochastic dynamical systems," CHAOS 18, 023122 (2008). PDF
- Lora Billings, Ira B. Schwartz, and Leah B. Shaw, "The Dynamics of Antibody Dependent Enhancement in Multi-Strain Diseases with Vaccination," Proceedings from Frontiers in Applied and Computational Mathematics 2008, New Jersey Institute of Technology, World Scientific.
- Lora Billings, Amy Fiorillo, and Ira B. Schwartz, "Vaccinations in disease models with antibody-dependent enhancement," Mathematical Biosciences, 211/2 (2008) 265-281. PDF
- Leah B. Shaw, Lora Billings, and Ira B. Schwartz, "Using dimension reduction to improve outbreak predictability of multistrain diseases," Journal of Mathematical Biology, 55 (2007) 1-19. PDF
- Lora Billings, Ira B. Schwartz, Leah B. Shaw, Marie McCrary, Donald S. Burke and Derek A.T. Cummings, "Instabilities in multiserotype disease models with antibody-dependent enhancement," Journal of Theoretical Biology, 246 (2007) 18-27. PDF
- Ira B. Schwartz and Lora Billings, "Fluctuation Induced Almost Invariant Sets," Naval Research Laboratory Memo Report NRL/MR/6790--0609012 (2006).
- D.A.T. Cummings, I. B. Schwartz, L. Billings, L. B. Shaw, and D. S. Burke, "Dynamic Effects Of Antibody Dependent Enhancement On The Fitness Of Viruses," Proceedings of the National Academy of Sciences 102 (2005) 15259-15264. PDF
- I. B. Schwartz, L. B. Shaw, D.A.T. Cummings, L. Billings, M. McCrary, and D. Burke, "Chaotic desynchronization of multi-strain diseases," Physical Review E 72, 066201 (2005). PDF
- Carmen Piccolo and Lora Billings, "The Effect of Vaccinations in an Immigrant Model," Mathematical and Computer Modelling 42 (2005) pp. 291-299.PDF
- I. B. Schwartz, L. Billings, D. S. Morgan, and Y.-C. Lai, "Noise induced dimension changing bifurcations," Proceedings from SPIE: Noise in Complex Systems and Stochastic Dynamics (2005). PDF
- W.-w. Tung, Y. Qi, J.B. Gao, Y. Cao, L. Billings, "Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity," Chaos, Solitons, and Fractals, 24 (2005) pp. 645-652. PDF
- I.B. Schwartz, L. Billings, and E.M. Bollt, "Dynamical epidemic suppression using stochastic prediction and control," Physical Review E 70, 046220 (2004). PDF
- L. Billings, I.B. Schwartz, D.S. Morgan, E.M. Bollt, R. Meucci, and E. Allaria, "Stochastic bifurcation in a driven laser system: Experiment and theory," Physical Review E 70 026220 (2004). PDF
- I. B. Schwartz and L. Billings, "Stochastic Epidemic Outbreaks: Why Epidemics Are Like Lasers," Proceedings from SPIE: Noise in Complex Systems and Stochastic Dynamics 5471 (2004) pp. 266-279. PDF
- I. B. Schwartz, D. S. Morgan, L. Billings, and Y.-C. Lai, "Multi-scale continuum mechanics: From global bifurcations to noise induced high dimensional chaos," CHAOS 14:2 (2004) pp. 373-386. PDF
- R. Meucci, D. Cinotti, E. Allaria, L. Billings, I. Triandaf, D. Morgan, and I.B. Schwartz, "Global manifold control in a driven laser: sustaining chaos and regular dynamics," Physica D, 189:1-2 (2004) pp. 70-80. PDF
- L. Billings, E. M. Bollt, D. S. Morgan, and I. B. Schwartz, "Stochastic global bifurcation in perturbed Hamiltonian systems," Discrete and Continuous Dynamical Systems, Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, May 24-27, 2002, Wilmington, NC, supplemental volume, 123-132 (2003). PDF
- Ira Schwartz, Lora Billings, David Hollt, Anne Kusterbeck, and Ioana Triandaf, "Chemical and biological sensing -- Modeling and analysis from the real world," to be included as a chapter of the book "Mathematical and Modeling Approaches in Homeland Security," to be published in SIAM's series Frontiers in Applied Mathematics, co-edited by Tom Banks and Carlos Castillo-Chavez (2003).
- Y.-C. Lai, Z. Liu, L. Billings, and I. B. Schwartz, "Noise-induced unstable dimension variability and transition to chaos in random dynamical systems," Physical Review E 67 (2003), art. no. 026210. PDF
- E. M. Bollt, L. Billings, and I. B. Schwartz, "A manifold independent approach to understanding transport in stochastic dynamical systems," Physica D 173 (2002), pp. 153-177. PDF

To see a movie of the PDF for the MSI model as the standard deviation of the noise is increased, click here - L. Billings, E. M. Bollt, and I. B. Schwartz, "Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus Spread," Physical Review Letters 88 (2002), art. no. 234101. PDF
- L. Billings, W. M. Spears, and I. B. Schwartz, "A Unified Prediction of Computer Virus Spread in Connected Networks," Physics Letters A, 297 (2002), pp. 261-266. PDF
- Z. Liu, Y.-C. Lai, L. Billings, and I. B. Schwartz, "Transition to chaos in continuous-time random dynamical systems," Physical Review Letters 88 (2002), art. no. 124101. PDF
- L. Billings and I. B. Schwartz, "Exciting chaos with noise: unexpected dynamics in epidemic outbreaks," Journal of Mathematical Biology 44 (2002), pp. 31-48. PDF
- I. B. Schwartz, L. Billings, J. J. Pancrazio, and J. M. Schnur, "Methods for short time series analysis of cell-based biosensor data," Biosensors & Bioelectronics 16 (2001), pp. 503-512. PDF
- L. Billings and E. M. Bollt, "Probability density functions of some skew tent maps," Chaos, Solitons and Fractals, 12 (2001), pp. 365-376. PDF
- W. M. Spears, L. Billings, and I. B. Schwartz, Modeling Viral Epidemiology, Naval Research Laboratory Memo Report, NRL/MR/6700--01-8537 (2001).
- L. Billings, I. B. Schwartz, J. J. Pancrazio, and J. M. Schnur, "Dynamic and geometric analysis of short time series: a new comparative approach to cell-based biosensors," Physics Letters A, 286 (2001), pp. 217-224.
- T. W. Carr, L. Billings, I. B. Schwartz and I. Triandaf, "Bi-instability and the global role of unstable resonant orbits in a driven laser," Physica D, 147 (2000), pp. 59-82. PDF
- L. Billings, J. H. Curry and V. Robins, "Chaos in Relaxed Newton's Method: The Quadratic Case," Contemporary Mathematics, 252 (1999), pp. 63-70. PDF
- L. Billings, J. H. Curry and E. Phipps, "Symmetric Functions and Exact Lyapunov Exponents," Physica D, 121 (1998), pp. 44-64. PDF
- L. Billings, J. H. Curry and E. Phipps, "Lyapunov Exponents, Singularities and a Riddling Bifurcation," Physical Review Letters, 79 (1997), pp. 1018-1021. PDF
- L. Billings and J. H. Curry, "On Noninvertible Mappings of the Plane: Eruptions," CHAOS, 6(1996), pp. 108-120. PDF
- L. Billings and J. H. Curry, Bifurcations in a Class of Noninvertible Mappings of the Plane. Proceedings from CESA '96 IMACS Multiconference: Computational Engineering in Systems Applications held in Lille, France. 2 (1996), pp. 625-629.

COLLEGE OF SCIENCE AND MATHEMATICS | MSU

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