Research

 

The Fear of the Lord is the beginning of wisdom, and knowledge of the Holy One is understanding. (Proverb 9:10)

 

Research Interests:

My research interests include mathematical biology, computational 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 and Control ( Lyme Disease: Ticks and Hosts; Rabies in Raccoons; Discrete Model; Antibiotic-resistant bacteria: Methicillin-resistant Staphylococcus aureus (MRSA); Malaria using sterile insect technique (SIT) )
  • Natural Resource Management ( Fisheries: General Population, Atlantic Cod; NTFP: non-timber forest products; Algae/Ulva management)
  • Systems Biology ( Modulation of Macrophage Inflammatory Signaling by Intracellular Cryptococcus neoformans )

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.


Research Work:

 


   Current Work:

  • F. Agusto, R. Florida and W. Ding.
    Mathematical model of community-associated and hospital-associated Methicillin-resistant Staphylococcus aureus transmission in community settings, 2017. 
  • L. Cai , J. Summers and W. Ding.
    Optimal control of sterile mosquitos for Malaria, 2017 (Student Funded by URECA 2017).
  •  V. Hrynkiv, M. Saum and W. Ding.
    Optimal Control applied to Competition and Mutualism in a PDE system, 2017.
  • Guest Editor (with R. Fister, R. Salinas, R. Leander, E. Numfor, D. Burton)
    Special Issue in honor of Suzanne Lenhart's 65th Birthday, Journal of Natural Resource Modeling, 2017-18.
  • R. Florida, J. Summers, P. Nepal and W. Ding.
    Experience and Lessons Learned from Using SIMIODE Modeling Scenarios, 2017. 
    Developing Python Notebook and documents for the usage of SIMIODE modeling scenarios.
  • B. Bartel. W. Ding, J. Eller, J. Iriarte-Gross, K. Petersen, G. Webber, M. Hein, D. Meyerink.
    Advancing the participation and advancement of women in STEM Careers at MTSU, 2017.
  • T. Brinthaupt and W. Ding.
    MTSU Mid-Career Faculty Development Program, 2017.

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Other Work:

  1. Wandi Ding and Glenn Webb.
    Optimal Control Applied to Community-acquired Methicillin-resistant Staphylococcus Aureus in Hospitals, Journal of Biological Dynamics, 11:sup1, 65-78, 2017.  PDF
  2. James B. Hayes, Linda M. Sircy, Lauren E. Heusinkveld, Wandi Ding, Rachel N. Leander, Erin E. McClelland and David E. Nelson.
    Modulation of macrophage in ammatory NF-kB signaling by intracellular Cryptococcus neofor- mans, Journal of Biological Chemistry, 291:30, 15614-15627, 2016. DOI: 10.1074/jbc.M116.738187. PDF
  3. Orou G. Gaoue, Jiang Jiang, Wandi Ding, Folashade B. Agusto and Suzanne Lenhart.
    Optimal harvesting strategies for timber and non-timber forest products in tropical ecosystems, Theoretical Ecology, 9:3, 287-297, 2016. PDF
  4. Huili Ma, Hui Feng and Wandi Ding.
    Global asymptotic behavior of positive solutions for exponential form difference equations with three parameters, Journal of Applied Analysis and Computation, 6:3, 600-606, 2016. PDF
  5. Huili Ma, Hui Feng, Jiaofeng Wang and Wandi Ding.
    Boundedness and asymptotic behavior of positive solutions for difference equations of exponential form, Journal of Nonlinear Science and Applications, 8:5, 893-899, 2015.
  6. Wandi Ding.
    Fishery Harvesting: Atlantic Cod, Wandi Ding (2015), “1-70-T-FisheryHarvest,” Teacher Version Modeling Scenario at https://www.simiode.org/resources/1319, and Student Version at https://www.simiode.org/resources/1318, .
  7. Wandi Ding, Suzanne Lenhart and Horst Behncke.
    Discrete Time Optimal Harvesting of Fish Populations with Age Structure, Letters in Biomathematics, 1:2, 193-207, 2014. DOI: 10.1080/23737867.2014.11414480
  8. Wandi Ding, Raymond C. Hendon, Brandon Cathey, Evan Lancaster and Robert Germick.
    Discrete Time Optimal Control Applied to Pest Control Problems, Involve, a Journal of Mathematics 7-4 (2014), 479--489. DOI 10.2140/involve.2014.7.479
  9. 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.
  10. 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.
  11. 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.
  12. Wandi Ding and Suzanne Lenhart.
    Optimal Harvesting of a Spatially Explicit Fishery Model. Natural Resource Modeling, 22:2, 173-211, 2009.
    Poster at the 2007 World Conference on Natural Resource Modeling.
  13. 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, 2007.
  14. Wandi Ding.
    Optimal Control on Hybrid ODE Systems with Application to a Tick Disease Model. Mathematical Biosciences and Engineering , 4:4, 633-659, 2007.
  15. Grid Computing Project for Ecological Modeling and Spatial Control, 2006-07 (post-doctoral work)
  16. MTSU CBAS Faculty Research

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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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Grants:

  1. co-PI, NSF ADVANCE IT-Catalyst (NSF HRD #1409638):
    A Catalyst to ADVANCE the Participation and Advancement of Women in Academic STEM Careers at Middle Tennessee State University (with B. Bartel, J. Iriarte-Gross, J. Eller and K. Petersen), 2014-18.
    2015 ADVANCE Poster PDF,       2016 ADVANCE Poster PDF,       2017 ADVANCE Brochure PDF,        2017 White Paper PDF,              2017 ADVANCE Poster PDF
  2. MTSU LT&ITC Faculty Learning Community (FLC): Mid-Career Faculty Development Program, (with D. Raffo, G. Webber, R. Henderson, R. Otter and T. Brinthaupt), 2014.
  3. MTSU Instructional Technologies Innovation Grant (ITI) (with Z. Sinkala and R. Leander), 2014.
  4. MTSU Instructional Evaluation and Development Grant (IED), 2011.
    To design and implement of a pilot program training for undergraduates in biological and mathematical sciences.
  5. Faculty Research and Creative Activities (FRCAC), MTSU, August 2009- May 2010.
    Optimal Control Applied to Native-Invasive Population Dynamics via a PDE Model
  6. NSF STEP (Stepping Up Undergraduate Research) Summer Reseach, MTSU, June-July 2009.
    Mathematical Modeling and Control of Populations: Application in Biological Pest Control
  7. Faculty Research and Creative Activities (FRCAC), MTSU, August 2008- May 2009.
    Optimal Harvesting of Fish Populations with Age Structure
  8. MTSU Distinguished Lecture Fund: 2009, 2010, 2011, 2012.
  9. Travel grants:
    -  Society for Mathematical Biology (SMB) grant to support our special session in the AMS Southeastern Spring Sectional Meeting (March 27-29, 2015), 2014.
    -  Society of Mathematical Biology (SMB) Travel grant 2011.
    -  SIAM-NSF Postdoc/Early Career Travel Award 2010.
    -  AWM-NSF Travel Grants for Women Researchers 2009.

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 Professional Development (Conferences/Workshops)

           Selected Invited Conferences/Presentation

  1. AMS Special session on Recent Advances in Mathematical Biology, Nashville, TN, April 14-15, 2018.
  2. AMS Special Session on Analytical and Computational Advances in Mathematical Biology Across Scales, Columbus, OH, March 17-18, 2018.
  3. AMS Special Session on Differential Equations and Applications, Columbus, OH, March 17-18, 2018.
  4. The Fields Institute for Research in Mathematical Sciences Workshop on Human-Environment Systems: Feedback and Management, Toronto, Canada, March 5-9, 2018.  Flyer
  5. AMS Speical Session on Modeling in Differential Equations - High School, Two-year College, Four-Year Institution, Joint Mathematics Meetings (JMM), San Diego CA, January 10-13, 2018.
  6. International Conferences on Mathematical Modelling and Analysis of Populations in Biological Systems (ICMA VI), the 6th (ICMA-VI) will be held at the University of Arizona, in Tucson, Arizona, October 20-22, 2017.
  7. Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Arizona State University, October 19, 2017.
  8. The 37th Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE 2017), Kennesaw State University, October 7-8, 2017. (Chair of the Parallel Session Sunday 1:30-2:50pm )
  9. Vanderbilt University, Department of Mathematics, PDE seminar, September 8, 2017.
  10. Banff International Research Station for Mathematical Innovation and Discovery (BIRS) workshop on Women in Control: New Trends in Infinite Dimensions, Banff, Canada, July 16-21, 2017. Link for Video and PPT 
  11. International Conference on Reaction-Diffusion Equations and Their Applications to the Life, Social and Physical Sciences, Beijing, China, May 26-29, 2016.
  12. Ocean University of China (OUC), School of Mathematics Colloquium, June 9, 2015.
  13. Qingdao University (QD), China, School of Mathematics Colloquium, June 4, 2015.
  14. 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.
  15. University of Tennessee - Chattanooga (UTC), Department of Mathematics Colloquium, June 9, 2014.
  16. 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.
  17. Mathematical Biosciences Institute (MBI) workshop 2 on Rapid Evolution and Sustainability, Optimal control of models to sustain populations, Columbus, OH, October 7-11, 2013.
  18. 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.
  19. American Mathematical Society (AMS) Special Session at the Joint Mathematics Meetings (JMM): Control of Biological and Physical Systems, Boston, MA, Jan. 2012.
  20. The Third International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems (ICMA III), San Antonio, TX, Oct. 2011.
  21. 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.
  22. The Second International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems (ICMA II), Huntsville, AL, October, 2009.
  23. 2009 Society of Industrial and Applied Mathematics (SIAM) Conference on Control and Its Applications, Denver, CO, July, 2009.
  24. American Mathematical Society (AMS) regional conference, Huntsville, AL, October, 2008.
  25. Special Session on Applied Partial Differential Equations at American Mathematical Society (AMS) Southeastern meeting, Murfreesboro, TN, November, 3-4, 2007.

           NSF ADVANCE IT-Catalyst Grant Presentations

  • Middle Tennessee State University ADVANCE: Spotlight on Changing the Institutional Culture to Improve the Recruitment, Retention, and Advance of Women STEM Faculty, MTSU Scholars Week, March 30, 2017.
  • Campus Climate Survey and Focus Group Results Presentation, November, Murfreesboro, TN, 2015.
  • ADVANCEing STEM Careers for Women at MTSU, 35th Annual Conference, Women in Higher Education in Tennessee, October 23, Murfreesboro, TN, 2015.

           Selected Workshops/Faculty Development

  1. The Fields Institute for Research in Mathematical Sciences Workshop on Human-Environment Systems: Feedback and Management, Toronto, Canada, March 5-9, 2018.
  2. Grant Writing Enhancement Program at MTSU 2017.
  3. Banff International Research Station for Mathematical Innovation and Discovery (BIRS) workshop on Women in Control: New Trends in Infinite Dimensions, Banff, Canada, July 16-21, 2017.
  4. IMA Annual Program Year Workshop: Biological Systems and Networks, November 16-20, Minneapolis MN, 2015. 
  5. MAA-PREP Workshop: Systemic Initiative for Modeling Investigation and Opportunities with Differential Equations (SIMIODE), July 19-25, Helena, MT, 2015.
  6. Invited Participant: Investigative Workshop on Interface Disease Models, National Institute for Mathematical and Biological Synthesis (NIMBioS), Knoxville, TN, March 11-13, 2014.
  7. 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, 2013.
  8. Invited Participant: “Mid-Career Faculty Development” Faculty Learning Community, MTSU 2013-14.
  9. The Importance of Mentoring and Work-Life Satisfaction Workshop, Association of Women in Science (AWIS), MTSU, March 18-20, 2013.
  10. Global South Summit, Nashville, TN, November 13-14, 2012
  11. XSEDE (Extreme Science and Engineering Discovery Environment) Nashville Regional Workshop, Vanderbilt University, Nashville, TN, May 7-8, 2012
  12. 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
  13. Conference Board of the Mathematical Sciences (NSF - CBMS ) Lecture Series on Mathematical Epidemiology with Applications, Johnson City, TN, July 25-29, 2011. 
  14. Numbers Count Workshop --- NIMBioS, BioQuest and HHMI, 2009
  15. 2007 Workshop for Young Researchers in Mathematical Biology (WYRMB)
  16. Computational Science Workshop for Natural Resource Managers 2007 
  17. Association of Women in Mathematics (AWM) Workshop for Women Graduate Students and Recent PhDs, New Orleans, LA, January, 2007.
  18. Computational Science Workshop for Natural Resource Managers 2006 
  19. 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.
  20. Joint Institute for Computational Science (JICS) workshop on Parallel Programming with MPI, University of Tennessee, May 2004.
  21. Mathematical Biological Complexity Short Course, University of Tennessee, July 2003.

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 Conference/Session/Mini-Symposium Organized

  1. SCUDEM 2018 (National Student Competition Using Differential Equations Modeling)

    Dr. Ding is the local host for Middle Tennessee State University (MTSU) site for National Student Competition Using Differential Equations Modeling - SCUDEM 2018.

    SCUDEM takes place over a week-long period that begins on each team's individual home campus and culminates on Saturday, 21 April 2018, 8:30 AM-4:30 PM, at a regional host site in the United States and beyond.

    Dr. Ding serves as Faculty Coach and have been training the student team from summer 2017 to spring 2018.

  2. American Mathematical Society (AMS) Southeastern Spring Sectional Meeting, Special Session on Recent Trends in Mathematical Biology, Huntsville, AL, March 27-29, 2015. (Co-organize with Z. Sinkala)
  3. 2014 SIAM Conference on the Life Sciences, Minisymposium on Mathematical Modeling and Control of Ecological and Epidemiological Problems (MS 66 & 74). Charlotte, NC, August 4-7, 2014. (Co-organized with R. Leander)
  4. American Mathematical Society (AMS) Southeastern 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. (Co-organized with R. Fister)
  5. AMS Special Session at the Joint Mathematics Meetings: Control of Biological and Physical Systems, Boston, MA, January 2012. (Co-organized with S. Lenhart and V. Hrynkiv)

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Resources:

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