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 ; Generic; Antibiotic-resistant bacteria: Methicillin-resistant Staphylococcus aureus (MRSA) )
• Natural Resource Management ( Fisheries: Generic , Cod; NTFP: non-timber forest products )

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.

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Research Work:

• Current Work
• Other Work
• Dissertation
• Workshops/Faculty Development
• Grants
• Conference Session Organized

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1. W. Ding, C. Hendon, B. Cathey, E. Lancaster and R. Germick
   Discrete Time Optimal Control Applied to Pest Control Problems, submitted 2012.
2. Wandi Ding, Volodymyr Hrynkiv and Xiaoyu Mu
   Optimal Control Applied to Native-Invasive Species Competition via a PDE Model, Electronic Journal of Differential Equations, Vol. 2012, 237:1-18, 2012.
   
3. Wandi Ding and Suzanne Lenhart.
   An Introduction to Optimal Control for Discrete Models with an Application to Disease Modeling. Modeling Paradigms and Analysis of Disease Transmission Models, 109-119, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 75, Amer. Math. Soc., Providence, RI, 2010.
   
4. W. Ding, Suzanne Lenhart, Heather Finotti, Yuan Lou and Yuquan Ye.
   Optimal Control of the Growth Coefficient on a Steady State Population Model. Nonlinear Anal. Real World Appl. 11, 688-704, 2010.
   
5. Wandi Ding and Suzanne Lenhart.
   Optimal Harvesting of a Spatially Explicit Fishery Model. Natural Resource Modeling, 22:2, 173-211, May, 2009.
   

   Poster at the 2007 World Conference on Natural Resource Modeling.

6. Wandi Ding, Louis Gross, Keith Langston, Suzanne Lenhart and Leslie A. Real.
   Rabies in Raccoons: Optimal Control for a Discrete Time Model on a Spatial Grid. Journal of Biological Dynamics, 1:4, 379-393, October 2007.
7. Wandi Ding.
   Optimal Control on Hybrid ODE Systems with Application to a Tick Disease Model. Mathematical Biosciences and Engineering , 4:4, 633-659, October 2007.
8. Grid Computing Project for Ecological Modeling and Spatial Control, 2006-07 (post-doctoral work)
9. Shusen Xie and Wandi Ding
   Linear Modified Finite Difference Method Combined with Characteristics for Convection-Diffusion Problems. J. Qingdao University of Science & Technology, No.2, 9-13, 2002
   
   
10. M.S. Thesis: Wandi Ding
    "Linear Modified Finite Difference Method for a Type of Initial Value Problems of Parabolic Partial Differential Equations." Ocean University of Qingdao, China, 2001, Library collection code: Y406018
    
    
11. Shusen Xie and Wandi Ding
    "Optimal Numerical Primitive Function Formula in the space W(p;B)" (Preprint, 2002)
    

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Dissertation:

Two Biological Applications of Optimal Control to Hybrid Differential Equations and Elliptic Partial Differential Equations

Advisor: Dr. Suzanne Lenhart

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Professional Development:

1. The Importance of Mentoring and Work-Life Satisfaction Workshop, Association of Women in Science (AWIS), MTSU, March 18-20, 2013.
2. Global South Summit, Nashville, TN, November 13-14, 2012.
3. XSEDE (Extreme Science and Engineering Discovery Environment) Nashville Regional Workshop, Vanderbilt University, Nashville, TN, May 7-8, 2012.
4. 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.
5. Conference Board of the Mathematical Sciences (NSF-CBMS ) Lecture Series on Mathematical Epidemiology with Applications, Johnson City, TN, July 25-29, 2011.
6. Numbers Count Workshop --- NIMBioS, BioQuest and HHMI, 2009
7. 2007 Workshop for Young Researchers in Mathematical Biology (WYRMB)
8. Computational Science Workshop for Natural Resource Managers 2007 (invited speaker)
   
9. Computational Science Workshop for Natural Resource Managers 2006 (invited speaker)
   
10. 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.
    
    
11. Joint Institute for Computational Science (JICS) workshop on Parallel Programming with MPI, University of Tennessee, May 2004.
12. Mathematical Biological Complexity Short Course, University of Tennessee, July 2003.

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1. MTSU Instructional Evaluation and Development Grant (IED), 2011.
   To design and implement of a pilot program training for undergraduates in biological and mathematical sciences.

2. Faculty Research and Creative Activities (FRCAC), MTSU, August 2009- May 2010.
   Optimal Control Applied to Native-Invasive Population Dynamics via a PDE Model
3. NSF STEP (Stepping Up Undergraduate Research) Summer Reseach, MTSU, June-July 2009.
   Mathematical Modeling and Control of Populations: Application in Biological Pest Control
4. Faculty Research and Creative Activities (FRCAC), MTSU, August 2008- May 2009.
   Optimal Harvesting of Fish Populations with Age Structure
5. MTSU Distinguished Lecture Fund: 2009, 2010, 2011, 2012.
6. Travel grants:

• Society of Mathematical Biology (SMB) Travel grant 2011.
• Conference Board of the Mathematical Sciences (NSF-CBMS) Lecture Series travel funds 2011.
• SIAM-NSF Postdoc/Early Career Travel Award 2010.
• AWM-NSF Travel Grants for Women Researchers 2009.

1. Simons Foundation Collaboration Grants for Mathematicians, submitted 2013.
2. Co-PI, NIH-R15: Mathematical Modeling of Cell Motility and Proliferation in Cancer ( PI: Z.Sinkala), submitted February 2012.
3. Elsevier Foundation New Scholars Program:
   PI, Building and Sustaining a Middle TN Learning Community for Women and Underrepresented Minorities in STEM, submitted August 2011.
4. NSF-DMS-PRISM:
   co-PI, MT-Proactive Recruitment in science and mathematics: Integrating Math and Biology in Middle Tennessee, submitted March 2010.
   PI: G. Rowell, other co-PIs: L. Green, R. Seipelt and Z. Sinkala.
5. NSF-DMS-Math Biology (RUI):
   PI: Optimal Harvesting of Fishery Models with Age and Spatial Structures, submitted January 2010.

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1. AMS Special Session at the Joint Mathematics Meetings: Control of Biological and Physical Systems, Boston January 2012.

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