Tim Reluga

treluga at math-dot-psu-dot-edu

As of March 11, 2009

I am an assistant professor of mathematics at Penn State. My research interests concern the description, understand, and prediction of the dynamics of biological systems. This currently includes work in ecology, epidemiology, immunology, evolution, medicine, human behavior, and economics. I always have more projects and ideas going than I have time for, so I welcome emails from all students looking for interesting research projects.

Curriculum Vitae.

Publications

An SIS epidemiology game with two subpopulations. By T. Reluga.

Accepted to Journal of Biological Dynamics, February, 2009.
DOI Link, Preprint PDF.

The discounted reproductive number for epidemiology. By T. Reluga, J. Medlock, and A. Galvani.

Mathematical Biosciences and Engineering, 6 (2): 377-393, 2009.
This paper uses M-matrix theory, non-negative matrices, and Perron-Frobenius theory to establish some useful results regarding next-generation matrixes for population biology.
DOI Link, Preprint PDF.

Analysis of hepatitis C virus infection models with hepatocyte homeostasis. By T. Reluga, H. Dahari, and A. S. Perelson.

SIAM Journal on Applied Mathematics, 69 (4), 2009.
DOI Link, Preprint PDF.

Backward bifurcations and multiple equilibria in epidemic models with structured immunity. By T. Reluga, J. Medlock, and A. Perelson.

Journal of Theoretical Biology, 252 (1): 155-165, 2008.
DOI Link, Preprint PDF.

Optimal timing of disease transmission in an age-structured population. By T. Reluga, J. Medlock, E. Poolman, and A. Galvani.

Bulletin of Mathematical Biology, 69 (8): 2711-2722, 2007.
DOI Link, Preprint PDF.

Reservoir interactions and disease emergence. By T. Reluga, D. B. Walton, R. Meza, and A. Galvani.

Theoretical Population Biology, 72 (3): 400-408, 2007.
This paper contains some useful results on reducible branching processes and the multivariable form of L'Hopital's rule. L'Hopital's rule is particularly useful for multivariable generating functions because critical processes are sure to have a double root.
DOI Link, Preprint PDF.

Long-standing influenza vaccination policy is in accord with individual self-interest but not with the utilitarian optimum. By A. Galvani, T. Reluga, and G. Chapman.

Proceedings of the National Academy of Sciences, 104 (13): 5692-5697, March 27 2007.
DOI Link, Preprint PDF.

Resistance mechanisms matter in SIRS models. By T. Reluga and J. Medlock.

Mathematical Biosciences and Engineering, 4 (3): 553-563, July 2007.
Link.
Preprint PDF.

Evolving public perceptions and stability in vaccine uptake. By T. Reluga, C. Bauch, and A. Galvani.

Mathematical Biosciences, 204: 185-198, 2006.
DOI Link, Preprint PDF.

A model of spatial epidemic spread when individuals move within overlapping home ranges. By T. Reluga, J. Medlock, and A. Galvani.

Bulletin of Mathematical Biology, 68 (2): 401-416, February 2006.
This paper uses an Ornstein-Uhlenbeck process to describe spatial movement and obtains some asymptotic results for the speed of spatial spread of an epidemic. C++/Linux Code.
DOI Link, Preprint PDF.

On antibiotic cycling and optimal heterogeneity. By T. Reluga.

Mathematical Medicine and Biology, June 2005.
This paper studies generalizations of the Meissner equation to show how changes in antibiotic use may increase or decrease resistance prevalence.
DOI Link, Preprint PDF.

Nonequilibrium thermodynamics of a nonlinear biochemical switch in a cellular signaling process. By H. Qian and T. Reluga.

Physical Review Letters, 94: 028101, January 2005.
DOI Link, Preprint PDF.

Simulated evolution of selfish herd behavior. By T. Reluga and S. Viscido.

Journal of Theoretical Biololgy, 234 (2): 213-225, 2005.
C++/Linux Code.
DOI Link, Preprint PDF.

Stochasticity, invasions, and branching random walks. By M. Kot, J. Medlock, T. Reluga, and D. B. Walton.

Theoretical Population Biology, 66 (3): 175-184, 2004.
DOI Link, Preprint PDF.

A two-phase epidemic driven by diffusion. By T. Reluga.

Journal of Theoretical Biology, 229 (2): 249-261, July 21 2004.
This paper shows how a double-epidemic might emerge from a bioterrorism attack.
DOI Link, Preprint PDF.

Analysis of periodic growth-disturbance models. By T. Reluga.

Theoretical Population Biology, 66 (2): 151-161, September 2004.
DOI Link, Preprint PDF.

Miscellaneous

• Good and not-so-good Science fiction literature.
• Here is a good calculus problem from mathematical biology for undergraduates. It is about the optimal evolutionary shape of some seashells without spiraling (spiraling makes things MUCH harder).
• My favorite multi-dimensional integration formula.
• A gzipped tar archive example of the use of latex, foiltex, texpower, and pdfelatex for making presentations.
• An antique web paper I wrote ages ago(1995) on some mathematics done by the ancient Greeks. (It's incomplete, since I ran out of time before I got around to the cube-doubling problem.)

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