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NIMBioS Tutorial:

Optimal Control and Optimization for Biologists

Group photo.

Topic: Optimal Control and Optimization for Biologists

Meeting dates: December 15-17, 2009

Application deadline: October 15, 2009

Location: NIMBioS at the University of Tennessee, Knoxville

Organizers: Suzanne Lenhart (University of Tennessee, Department of Mathematics and NIMBioS Associate Director for Education, Outreach and Diversity); Michael Bevers (USDA Forest Service, Fort Collins, Colorado)

Objectives: This tutorial was designed to introduce selected topics in optimal control and optimization with an emphasis on biological applications. Introductory material on optimal control of ordinary differential equations and difference equations and some interactive computer labs was included in sessions led by Lenhart. Mathematical programming and spatial optimization techniques were demonstrated for managing natural resources under conditions of risk. Lectures and computer lab exercises introduced linear, integer, nonlinear, stochastic and chance-constrained programming methods in sessions led by Bevers.

Lectures and computer lab sessions were led by Lenhart Bevers. Renee Fister of Murray State University gave a lecture on optimal control techniques applied to cancer modeling. Paul Armsworth of the University of Tennessee gave a lecture on applications in conservation and natural resource management.

Evaluation Report (PDF)



Cho E. 2013. Algorithm for finding maximal frequent sets. International Journal of Pure and Applied Mathematics, 83(2). [Online]

Collins, C, Fister KR, Williams M. 2010. Optimal control of a cancer cell model with delay. Mathematical Modelling of Natural Phenomena, 5(3): 63-75. [Online]


Fister R, Buford G, Norris B, Lenhart S, Zhong P, Schaefer E, Gaff H. November 2010. Optimal control of cholera models. AMS Southeastern Section Meeting.


Cho E. 2010. Undergraduate Course: MAT 470 Mathematical Modeling. Kentucky State Univ., Frankfurt, KY.


Signoriello A. 2013. Undergraduate Honors Thesis: Stochastic models for an antibiotic-resistant infection. Ursinus College.

Velagala J. 2013. Undergraduate Honors Thesis: Markov chain based VRE model. Ursinus College.

Smith K. 2012. Undergraduate Honors Thesis: Modeling the effect of diversity in host plant-herbivore-predator interactions. Ursinus College.

Abdelmageed S. 2011. Undergraduate Honors Thesis: Uncertainty analysis of complex dynamical models. Ursinus College.

Tannenbaum L. 2011. Undergraduate Honors Thesis: Difference and differential equations models of Vancomycin-resistant Enterococci. Ursinus College.

Much K. 2010. Undergraduate Honors Thesis: Mathematical modeling and sensitivity analysis of antibiotic resistance. Ursinus College.

A goal of NIMBioS is to enhance the cadre of researchers capable of interdisciplinary efforts across mathematics and biology. As part of this goal, NIMBioS is committed to promoting diversity in all its activities. Diversity is considered in all its aspects, social and scientific, including gender, ethnicity, scientific field, career stage, geography and type of home institution. Questions regarding diversity issues should be directed to You can read more about our Diversity Plan on our NIMBioS Policies web page. The NIMBioS building is fully handicapped accessible.

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From 2008 until early 2021, NIMBioS was supported by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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