RESEARCH INTERESTS
 Numerical Analysis
Numerical Solution of
Ordinary and Partial Differential Equations/Systems:
Nonstandard Finite Difference Methods
 Mathematical Biology
Mathematical Modeling and Analysis of Complex Biological Systems: Microbial Biofilms, Population Interactions, Bone Formation and Growth, and the Human Immune System
My main scientific research covers the fields of mathematical biology and numerical analysis. It is strongly motivated and oriented toward applications. I am primarily interested in the accurate mathematical modeling and theoretical analysis of biological phenomena, in particular the modeling of population dynamics, microbial biofilms, bone formation and growth, and the human immune system. I am also interested in the formulation, analysis and implementation of nonstandard numerical methods for solving nonlinear differential equations.
CURRENT RESEARCH PROJECTS
 ``Mathematical Modeling and Simulation of Bone Remodeling''
(in collaboration with
A. Adnan,
Mechanical & Aerospace Engineering, and P. Aswath, Materials Science and Engineering, and B. ChenCharpentier, Department of
Mathematics, University of Texas at Arlington)
 ``Nonstandard FiniteDifference Methods for Dynamical Systems with Applications in
Mathematical Biology''
(in collaboration with
D. Dimitrov,
Fred Hutchinson Cancer Research Center; and R. Anguelov, Department of
Mathematics, University of Pretoria, South Africa).
 ``Mathematical Modeling, Numerical Simulation, and Visualization of Biomedical ImplantAssociated Infections''
(in collaboration with Liping Tang, Department of Bioengineering, B. ChenCharpentier, Department of
Mathematics, University of Texas at Arlington;
Alicia Prieto Langarica, Department of
Mathematics and Statistics, Youngstown State University;
and N. Sirakov, Departments of Mathematics and Computer Science, TAMU  Commerce)
RESEARCH, EDUCATION, EQUIPMENT, AND TRAVEL GRANTS:
AWARDED RESEARCH AND EDUCATION GRANTS:
 9/20158/2018; ``GAANN Fellowships in Mathematics at University of Texas at Arlington'' (CoPI; T Aktosun, PI; J. Su, D. Jorgensen, R. Gornet, CoPIs), U.S. Department of Education, Ref:
P200A150062 (Total Amt.: $922,746.00)
 9/20138/2017; ``Scholarships for Undergraduates to Reach Goals in Education (SURGE)'' (CoPI; T. Aktosun, PI; R. Gornet, B. Shipman, J. Su, CoPIs), National Science Foundation, Ref:
DUE1260019 (Total Amt.: $623,608.00)
 7/20146/2015; ``Building Bridges to the Balkans  Mathematical Biology in Sofia 2014'' (PI;
M. Mincheva, A. Prieto Langarica, P. Hinow, CoPIs), National Science Foundation, Ref: DMS1401667 (Total Amt.: $20,000.00)
 4/20095/2015; ``GK12: Mathematically Aligned Vertical Strands Connecting Mathematics
Research, Pedagogy and Outreach for GK12 Fellows and Teachers (MAVS
Project)'' (CoPI; M. Cordero, PI; J. Su, J. Epperson, T. Jorgensen, CoPIs;
T. Aktosun, J. Zhu, Former CoPIs), National Science Foundation, Ref: DGE0841400 (Total Amt.: $2,854,024.00)
 9/20088/2014; ``UBMInstitutional: Undergraduate Training in Theoretical Ecology Research
(UTTER)'' (PI; J. Grover, L. Gough, C. Kribs Zaleta, L. Mydlarz, CoPIs; D.L. Hawkins, FA), National Science Foundation, Ref: DUE0827136 (Total Amt.: $780,946.00).
 6/20085/2013; ``Scholarships for Undergraduates to Reach Goals in Education (SURGE)'' (CoPI;
J. Zhu, PI; T. Aktosun, R. Gornet, B. Shipman, CoPIs), National Science Foundation, Ref: DUE0807110
(Total Amt.: $483,000.00)
 8/20095/2010; ``TensorSUMMA Grant: Strengthening Underrepresented Minority Mathematics Achievement'' (CoPI; D. Grantcharov, PI), Mathematical Association of America,
Tensor Foundation (Total Amt.: $6,000.00).
 09/200108/2002; ``IGMS:
Modeling Microbial Populations, Biofilms and Competition Dynamics
in a General Gradostat'' (PI; J. Grover, N. Smatresk, CoPIs),
National Science Foundation,
Ref: DMS0107439
(Total Amt.: $99,998.00).
 9/20018/2002; ``Mathematical and Computational Methods for Modeling of Subsurface Biobarrier
Persistence in the Presence of Protozoa'' (PI), UT Arlington, Ref: REP14748717
(Total Amt.: $8,200.00).
AWARDED EQUIPMENT AND TRAVEL GRANTS:
 Computational Sciences Research Equipment, The University of Texas at Arlington  Integrative Computational Sciences (ICOMPS) Alliance (10/2008, Total Amt.: $11,318.19).
 2007 AMSMAA Joint Mathematics Meeting: ``Diversity Initiative Grant'', The
Mathematical Association of America  Committee on Student Activities and
Chapters (12/2006, Total Amt.: $500.00).
 AMS Conference: ``Mathematical Challenges of the 21st Century'', American
Mathematical Society  National Science Foundation
(8/2000, Total Amt.: $1,000.00).
 IMA Workshop: ``Confinement and Remediation of Environmental Hazards'', Institute
for Mathematics and its Applications  National Science Foundation
(1/2000, Total Amt.: $1,500.00).
 ``GrantinAid for Foreign Studies'', EVRIKA Foundation, Bulgaria (1/1995, Total Amt.: $200.00).
GRADUATE STUDENT SUPERVISIONS
CURRENT PH.D. STUDENTS:

Iris Alvarado, Ph.D. Student, UT Arlington
Research Project: ``Mathematical Modeling of Bone Remodeling''


Imelda Trejo Lorenzo, Ph.D. Student, UT Arlington
Research Project: ``The Mathematics of Bone Fracture Repair''

PH.D. DISSERTATIONS DIRECTED:

Daniel Wood, Ph.D., UT Arlington, 7/2015
Dissertation Title: ``Advancements and Applications of Nonstandard Finite Difference Methods ''
Current Position: Postdoctoral Research Scholar, Vaccine and Infectious Disease Division,
Fred Hutchinson Cancer Research Center, Seattle, WA


Xiaoyang Dong, Ph.D., UT Arlington, 7/2013
Dissertation Title: ``Mathematical Models of Nutrient Recycling and Toxin Production in a Gradostat''
Current Position: Senior Associate (Analyst), Phoenix Analytics Center,
Discover Financial Services, Phoenix, AZ


Alicia Prieto Langarica, Ph.D., UT Arlington, 7/2012
Dissertation Title: ``From Discrete to Continuous Models of Cell Movement: An Application to Medical Implants''
Current Position: Assistant Professor, Department of Mathematics and Statistics,
Youngstown State University, Youngstown, OH


Ian P. Martines, Ph.D., UT Arlington, 4/2008
Dissertation Title: ``Mathematical Analysis of Allelopathy and Resource Competition Models''
Current Position: Associate Professor and Chair, Mathematics Department,
St. Mary's University, San Antonio, TX


Dobromir T. Dimitrov, Ph.D., UT Arlington, 4/2005
Dissertation Title: ``Nonstandard FiniteDifference Methods
for Dynamical Systems with Applications in Mathematical Biology''
Current Position: Senior Staff Scientist, Vaccine and Infectious Disease Division,
Fred Hutchinson Cancer Research Center, Seattle, WA


Hilaire M. Kadjo, Ph.D., UT Arlington, 4/2004
Dissertation Title: ``An AgeStructured Population Model: Interactions Between
Nutrients and Phytoplankton''
Current Position: Senior Systems Engineer, Network Centric Systems, ITAS,
Raytheon Company, Plano, TX

M.S. SPECIAL PROJECTS / THESES DIRECTED:
 Huda Amer Hadi, M.S., UT Arlington, 8/2017
Thesis Title: ``A Mathematical Model of Hepatitis C Virus Infection Incorporating Immune Responses and Cell Proliferation''
 Robert Childress, M.S., UT Arlington, 11/2015
Thesis Title: ``Comparative Analysis of Various ContinuousTime Deterministic Models of TumorImmune Interactions''
 Alysmarie Hodges, M.S., UT Arlington, 5/2012
Thesis Title: ``Numerical Methods for Solving an HPV ODE Model''
 Tarik Celik, M.S., UT Arlington, 4/2012
Thesis Title: ``Comparison of Nonstandard Numerical Methods
for a Class of Initial Value Problems''
 Irfan Turk, M.S., UT Arlington, 7/2011
Thesis Title: ``A Mathematical Model of Swine Flu 2009 with Vaccination''
 Darren Sheets, M.S., UT Arlington, 4/2009
Thesis Title: ``Multiple Linear Regression Model
of Visceral Leishmaniasis in Bihar, India''
 Nithin Rahul, M.S., UT Arlington, 11/2005
Thesis Title: ``Interpolation of an Economic Model using the Newton's Method
and the Cubic Spline Method''
 Yonael Gebreyohannes, M.S., UT Arlington, 4/2005
Thesis Title: ``Numerical Simulation of MultiLane Traffic Flow''
 Sompoom Meechowna, M.S., UT Arlington, 11/2004
Thesis Title: ``Numerical Methods for a System of Partial Differential
Equations for Traffic Flow''
 Dobromir T. Dimitrov, M.S., UT Arlington, 7/2003
Thesis Title: ``Complete Mathematical Analysis of a PredatorPrey Model with a
BeddingtonDeAngelis Functional Response''
