Game dynamic model of social distancing while cost of infection varies with epidemic burden,
by Samit Bhattacharyya and Timothy Reluga.
IMA Journal of Applied Mathematics, September 21, 2018.
DOI:10.1093/imamat/hxy047, Preprint PDF.
Unintended Consequences and the Paradox of Control:
Management of Emerging Pathogens with Age-Specific Virulence, by
Spencer Carran, Matthew Ferrari, and Timothy Reluga.
PLoS Neglected Tropical Diseases 12(4): e0005997, April, 2018.
This is perhaps the first attempt out there to analyze a moderate-control
paradox in a time-dependent setting.
DOI:10.1371/journal.pntd.0005997, Preprint PDF.
Provisioning of public health can be designed to anticipate public
policy responses. By Jing Li, D. V. Lindberg, R. A. Smith,
and T. Reluga.
Bulletin of Mathematical Biology, 79(1) 163-190, January, 2017.
This is one of my favorite papers -- I think the mathematics is simple and
beautiful. But it was a 6 year ordeal to get it published. In
the mean time,
Wells et al, 2013 were expanding on our ideas, and Fenichel and Zhao,2014 have discussed further the ecological relevance of strategic complementarity and substituability.
DOI:10.1007/s11538-016-0231-8, Preprint PDF.
The importance of being atomic: ecological
invasions as random walks instead of waves,
by T. Reluga.
Theoretical Population Biology, December 2016, Volume 112, Pages 157-169.
- Some of the same techniques have been used by Yan and Feng (2010) to rank isolation and quarantine control performance. Amanda Ramacharan did a write-up on this for Penn State News, picked up by UPI and Science Daily.
Resource distribution drives the adoption of migratory, partially migratory, or residential strategies.
By T. Reluga and A. Shaw.
- Theoretical Ecology, March, 2015.
This is a beautiful little analysis of a spatially explicit seasonal migration model that shows how seasonality, movement costs, and resource heterogeneity can
conspire to drive co-existence, and potentially, speciation. A number of results can be obtained by hand, but there are also some open mathematical questions.
Population viscosity stops disease emergence by preserving local herd immunity. By T. Reluga and E. Shim.
- Proceedings of the Royal Society B , 281(1796), 20141901, October 22, 2014.
Covered in media by Johanna Ohm for CIDD and by Tanya Lewis for Livescience.com.
This is related to my earlier paper on risks from virus reservoirs.
Optimal migratory behavior in spatially-explicit seasonal environments. By Timothy Reluga and Allison Shaw.
- Discrete and Continuous Dynamical Systems - Series B October 9, 2014, 19(10), 3359-3378.
(Special issue in honor of Chris Cosner on the occasion of his 60th birthday, Submitted July, 2013).
I think this kind of model need some further attention. For example, I've
never been particularly happy with the economics idea of discounting, and my
work in this paper and my early paper on the discounted
reproductive number haven't asuaged my concerns. Somebody can probably
do a good job improving things with some density-dependent simulation models.
A reduction method for Boolean networks proven to conserve attractors. By Assieh Saadatpour, Reka Albert, and T. Reluga.
- SIAM Journal on Applied Dynamical Systems,
November, 2013, Volume 12, Issue 4, pp 1997-2011.
Equilibria of an Epidemic Game with Piecewise Linear Social Distancing Cost
By T. Reluga.
- Bulletin of Mathematical Biology October 2013, Volume 75, Issue 10, pp 1961-1984.
Games of age-dependent prevention of chronic infections by social distancing.
By T. Reluga and J. Li.
- Journal of Mathematical Biology, 2012.
A general approach to population games with application to vaccination. By
T. Reluga and A. Galvani.
- Mathematical Biosciences, 230 (2): 67-78, April, 2011.
(This paper received the 2013 Bellman Prize for best biannual paper)
Erratic flu vaccination emerges from short-sighted behaviour in contact
networks. By D. M. Cornforth, T. C. Reluga, E. Shim, C. T. Bauch, A. P.
Galvani, , and L. A. Meyers.
- PLOS Computational Biology, 7 (1): e1001062, 2011.
Game theory of social distancing in response to an epidemic. By T. Reluga.
- PLOS Computational Biology, 6 (5): e1000793,
The papers used differential game theory to find the equilibrium
behavior during an epidemic.
Branching processes and non-commuting random variables in population biology.
By T. Reluga.
- Canadian Applied Math Quarterly, 17 (2): 387, 2009.
Note: There are typos in Eq. 30 and Eq. 41 that are corrected in the
preprint version. The typos don't effect any of the subsequent calculations.
An SIS epidemiology game with two subpopulations. By T. Reluga.
- Journal of Biological Dynamics, 3 (5): 515-531, 2009.
Cressman et al, 2004 for some earlier discussion of related stability ideas.
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.
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):
This paper provides a complete bifurcation analysis of Harel's
for hepatitis C treatment responses, including formulas that can used to
predict clearance, partial infection, and bistability.
The analysis has been subsequently discussed by
DebRoy, Bolker, and Martcheva, 2009.
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.
One of the issues that bugged me when first learning mathematical epidemiology
was that it completely ignored the internal state of
the hosts changed because of immune responses. How did we know that theories which ignored the complexities of the immune response within individuals were adequate to explain population-scale dynamics? This paper is a step forward in resolving this by constructing some specific hypotheses and conditions.
(update 2012-08: Our results are nicely complementary to those in an earlier paper by
Hethcote, Yi, and Jing, 1999, which we were un-aware of in 2008.)
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.
This paper studies how age-dependent virulence can lead to a a
social-distancing game with two different Nash equilibria - one that
maximizes transmission and one that minimizes transmission. This is closely
related to the concept of ``endemic stability'' from veterinary science
and the paradox of moderate control in public health.
Polio is used as an illustrative example.
Reservoir interactions and disease emergence.
By T. Reluga, D. B. Walton, R. Meza, and A. Galvani.
- Theoretical Population Biology, 72 (3):
This paper provides a modelling framework for the study of disease-emergence pathways. This is a concrete approach to risk-assessment
associated with emergence patterns like those proposed by Wolfe et al..
It's model analysis contains some useful discussions of 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.
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.
Resistance mechanisms matter in SIRS models. By T. Reluga and J. Medlock.
- Mathematical Biosciences and Engineering, 4
(3): 553-563, July 2007.
This paper provides a resolution to a question of the time as to why
different models of immunity seemed to yield contradictory results.
Evolving public perceptions and stability in vaccine uptake. By T. Reluga,
C. Bauch, and A. Galvani.
- Mathematical Biosciences, 204: 185-198, 2006.
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. It provides a resolution to the problem of
whether spatial epidemic spread is governed by distributed
contacts or distribution of infected, without resorting to
Baysian melding approaches.
A more recent paper exploiting this idea to a different conclusion
is by Kenkre and Sugaya (2014). Also, the epidemic diffusion models and associated speed calculation can be traced back earlier to [Deterministic and stochastic models for recurrent epidemics](http://digitalassets.lib.berkeley.edu/math/ucb/text/math_s3_v4_article-04.pdf) by Bartlett, 1956.
Preprint PDF (fixes typo).
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
through resonance phenomena.
The same results apply to general habitat switching problems
in genetics (see
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.
Simulated evolution of selfish herd behavior. By T. Reluga and S. Viscido.
- Journal of Theoretical Biololgy, 234 (2): 213-225, 2005.
There's now a PNAS paper by Pearce et al.,2014
making a much bigger deal out of the same basic idea that Steve and I were working on 10 years ago.
Morrell,2014 accuses us of only considering
"equilibrium" domains of danger, but that's wrong -- we varied the delay between warning
and attack from zero (no warning) to infinity, and there was certainly no "equilibrium" when the warning was zero
(not to say that our model didn't have limitations).
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.
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. In an important special case, travelling epidemic waves
can emerge even when only driven by a bioterrorism agent in 1 or 2 dimensions.
This is a pretty strange effect, and yet another example of how 3 dimensions are
special. This also provides an explanation of anomolous travelling wave speeds
found by J. Cooke.
Weinberge, Lewis, and Li (2007) have since shown that reducible systems in general can
yield anomoulus spreading speeds.
Analysis of periodic growth-disturbance models. By T. Reluga.
- Theoretical Population Biology, 66 (2):
151-161, September 2004.