Lora Billings' Home Page

Dr. Lora Billings, Associate Professor
Department of Mathematical Sciences
Montclair State University
1 Normal Ave.
Montclair, N.J. 07043

My weekly schedule

Office: Richardson 247
Phone: (973) 655-7812
Fax: (973) 655-7686
Email: BILLINGSL@mail.montclair.edu

Classes: Find class information, handouts, and assignments on Blackboard
- Fall 2010:
  - MATH-112-01 PreCalculus, Mon/Wed 11:30AM-12:45PM,
    MATH-111-02 PreCalculus, Mon/Wed 1:00PM-2:40PM
  - MATH-495 Math Biology: Population Dynamics, Mon/Wed 10:00-11:15AM
- Spring 2011:
  - TBA
My Research Interests: Deterministic and Stochastic Dynamical Systems, Theory and Applications of Chaos, Ordinary Differential Equations, and Mathematical Biology and Epidemiology;
Publications
- Lucas Shaw, William M. Spears, Lora Billings, and Paul M. Maxim, "Effective Vaccination Policies," Information Sciences (2010), doi:10.1016/j.ins.2010.06.005. 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, 140601 (2010).
- 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
1 Normal Avenue, Montclair, N.J. 07043, USA (973) 655-4000