My research interests include mathematical biology, optimal control, mathematical modeling,
ordinary and partial differential equations, difference equations and hybrid systems
with applications to
- Population Dynamics ( Conservation Biology; Native-Invasive Species competition: cottonwood-salt cedar; Biological Pest Control )
- Disease Modeling ( Lyme Disease: Ticks and Hosts; Rabies in Raccoons;
Discrete Model; Antibiotic-resistant bacteria: Methicillin-resistant Staphylococcus aureus (MRSA);
Modeling and Simulation of NF-kB signaling for Parkinson's )
- Natural Resource Management ( Fisheries: General Population, Cod; NTFP: non-timber forest products; Optimal Plant Allocation )
Mathematical biology is a
growing branch of applied mathematics as the interest of modeling complex biological systems
increases. Optimal control theory is a branch of mathematics developed to find optimal
ways to control a dynamic system. Generally, the optimal control problem consists of an
objective functional, a dynamic system and the control(s). The controls enter the dynamics
in a variety of ways as coefficients, boundary terms or sources.
My research focuses on understanding the spatial and temporal patterns that arise in dynamic biological systems and
when possible, finding the best way to control the system.
Science Feb. 6th, 2004 --- Devoted to Mathematics in Biology
In a special collection of articles published beginning 6 February 2004, Science Magazine and
its online companion sites teamed up to explore one of the hottest interdisciplinary collaborations
in science today: the interface between mathematics and biology. In Science, News, Viewpoint, and
Review articles covered how mathematics and computation are informing biology on a wide variety of fronts,
the need for incorporating quantitative approaches into bioscience curricula, and some of the uses
-- and abuses -- of mathematical models for biological systems.
Two Biological Applications of Optimal Control to Hybrid Differential Equations and Elliptic Partial Differential Equations
Advisor: Dr. Suzanne Lenhart
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- Society for Industrial and Applied Mathematics (SIAM) Conference on the Life Sciences Mini-Symposium, Mathematical Modeling and Control of Ecological and Epidemiological Problems, Charlotte, NC, August 4-7, 2014.
- University of Tennessee - Chattanooga, Department of Mathematics Colloquium, June 9, 2014.
- American Mathematical Society (AMS) Southerneastern Spring Sectional Meeting, Special Session on Diversity in Modeling and Optimal Control: A
Celebration of Suzanne Lenhart's 60th Birthday, Knoxville, TN, March 21-23, 2014.
- Mathematical Biosciences Institute (MBI) workshop 2 on Rapid Evolution and Sustainability , Optimal control of models to sustain populations, Columbus, OH, October 7-11, 2013.
- American Mathematical Society (AMS) Special session on Mathematical Issues in Ecological and Epidemiological Modeling at the
South East Section of the meeting, Louisville, KY, October 5-6, 2013.
- American Mathematical Society (AMS) Special Session at the Joint Mathematics Meetings (JMM): Control of Biological and Physical Systems, Boston, MA, Jan. 2012.
- The Third International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems (ICMA III), San Antonio, TX, Oct. 2011.
- 2010 Society of Industrial and Applied Mathematics (SIAM) Conference on the Life Sciences, Mini-symposium on Optimal Control Applied to Biological Systems, Pittsburgh,
PA, July, 2010.
- The Second International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems, Huntsville, AL, October, 2009.
- 2009 Society of Industrial and Applied Mathematics (SIAM) Conference on Control and
Its Applications, Denver, CO, July, 2009.
- American Mathematical Society (AMS) regional conference, Huntsville, AL, October, 2008.
- Special Session on Applied Partial Dierential Equations at American Mathematical Society (AMS) Southeastern meeting, Murfreesboro, TN, November, 3-4, 2007.
- Invited Participant: Investigative Workshop on Interface Disease Models, National Institute for Mathematical and Biological Synthesis (NIMBioS), Knoxville, TN, March 11-13, 2014.
- Invited Speaker: Mathematical Biosciences Institute (MBI) workshop 2 on Rapid Evolution and Sustainability
, Optimal control of models to sustain populations, Columbus, OH, October 7-11,
- Invited Participant: “Mid-Career Faculty Development” Faculty Learning Community, MTSU 2013-14.
- The Importance of Mentoring and Work-Life Satisfaction Workshop, Association of Women in Science (AWIS), MTSU, March 18-20, 2013.
- Global South Summit, Nashville, TN, November 13-14, 2012.
- XSEDE (Extreme Science and Engineering Discovery Environment) Nashville Regional Workshop, Vanderbilt University, Nashville, TN, May 7-8, 2012.
- 5th Hands-on Workshop on Interrogating Cancer Resistance to Targeted Therapeutics with Systems Biology,
The Center for Cancer Systems Biology at Vanderbilt University (CCSB@V), Nashville, TN, August 22-24, 2011.
- Conference Board of the Mathematical Sciences (NSF-CBMS ) Lecture Series on
Mathematical Epidemiology with Applications, Johnson City, TN, July 25-29, 2011.
- Numbers Count Workshop --- NIMBioS, BioQuest and HHMI, 2009
- 2007 Workshop for Young Researchers in Mathematical Biology (WYRMB)
Computational Science Workshop for Natural Resource Managers 2007 (invited speaker)
- Association of Women in Mathematics (AWM) Workshop for Women Graduate Students
and Recent PhDs, New Orleans, LA, January, 2007.
Computational Science Workshop for Natural Resource Managers 2006 (invited speaker)
- Industrial Mathematical & Statistical Modeling (IMSM) Workshop @ NC State Univ. 2004
Natalie Almond, Wandi Ding, Xiaochuan Li, Xingtao Liu, Steven Rusnica, Ismael
Velzquez-Ramrez, Emily Lada, Fazafumi Ito, Michael Horton, Mellisa Choi.
"Mobile Sensing of Aerosolized Chemical and Biological Agents."
CRSC Technical Report, CRSC-TR04-41, 15-26, December, 2004.
- Joint Institute for Computational Science (JICS) workshop on Parallel Programming with MPI, University of Tennessee, May 2004.
- Mathematical Biological Complexity Short Course, University of Tennessee, July 2003.
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