
D M Bortz
From MathBio
Professional Information
Associate Professor in Applied Mathematics
BioFrontiers Task Force Member
IQBio Graduate Faculty
RASEI Affiliate
Vitae pdf
Google Scholar ORCID ResearchGate arXiv
Github repository
The primary research in my group is on mathematical biology, specifically
bacterial community population dynamics and biomechanics, cellular
migration, infectious diseases, and designs for an artificial pancreas. I
also have projects on information theoretic model selection,
computational experimental design, and probabilistic numerical
computations. These projects have been financially supported by NSF,
NIH, DOD, DOE, and NVIDIA.
Members of the group have gone to toptier graduate programs
(Berkeley, Caltech, Cambridge, Northwestern, Arizona, etc.) as well as
ended up in positions at researchoriented (U. Minnesota, SAMSI, U.
Adelaide, Air Force Research Lab) and teachingoriented (Harvey Mudd,
Olin College, Air Force Academy) institutions and in industry
(Mathworks). They have also won several national and international
awards, e.g., NSFGRFP (4), DOECSGF (1), DODNDSEG (1), and
GatesCambridge Fellowship (1).
For undergraduate and graduate students at the University of Colorado
who are interested in joining the group, please contact me directly and
attach a current resume.
Lastly, please note that at this time (1/2018) I have no postdoctoral
positions available.
Contact
 Note that I check my email once a day, typically in the early morning. For timesensitive issues, please call the main Applied Math office at (303) 4924668 and they will contact me.
 Email: dmbortz at colorado dot edu
 Campus Office: ECOT 234
 Postal Address:
Applied Mathematics University of Colorado, Box 526 Boulder, CO 803090526
Students (support in parenthesis)
Collaborators
Teaching
Publications
Preprints
 I. Mirzaev & D. M. Bortz. On the existence of nontrivial steadystate sizedistributions for a class of flocculation equations, (submitted). arXiv
 H.J. Dudley, L. Lu, Z.J. Ren, & D.M. Bortz. Sensitivity and Bifurcation Analysis of a DAE Model for a Microbial Electrolysis Cell, (submitted). arXiv
 S.H. Friedman, A.R.A. Anderson, D.M. Bortz, et al. MultiCellDS: A standard and a community for sharing multicellular data, (submitted). bioRxiv
 S.H. Friedman, A.R.A. Anderson, D.M. Bortz, et al. MultiCellDS: a communitydeveloped standard for curating microenvironmentdependent multicellular data, (submitted). bioRxiv
Refereed Articles & Book Chapters
 J.M. Wentz, A.R. Mendenhall, & D.M. Bortz. Pattern Formation in the LongevityRelated Expression of Heat Shock Protein16.2 in Caenorhabditis elegans, Bulletin of Mathematical Biology, (accepted). arXiv
 J.A. Stotsky, V. Dukic, & D.M. Bortz. A Point Process Model for Generating Biofilms with Realistic Microstructure and Rheology, Eur. J. Appl. Math., (accepted). doi arXiv
 J.T. Nardini & D.M. Bortz. Investigation of a Structured Fisher's Equation with Applications in Biochemistry, SIAM J. Appl. Math., 78(3), 1712–1736, 2018 doi arXiv
 E.P. Kightley, A. Pearson, J.A. Evans, & D.M. Bortz. Fragmentation of biofilmseeded bacterial aggregates in shear flow, Eur. J. Appl. Math., (accepted). doi arXiv
 V. Dukic & D.M. Bortz, Uncertainty Quantification Using Probabilistic Numerics: Application to Models in Mathematical Epidemiology, Inverse Problems in Science and Engineering, 28(2):223232, 2018 doi.
 I. Mirzaev & D.M. Bortz. A numerical framework for computing steady states of sizestructured population models and their stability, Mathematical Biosciences and Engineering, 14(4):933952, 2017. doi arXiv.
 D.M. Bortz, Characteristic roots for twolag linear delay differential equations, Discrete and Continuous Dynamical System  B, 21(8):24092422, Oct. 2016 doi.
 I. Mirzaev, E.C. Byrne, & D.M. Bortz. An Inverse Problem for a Class of Conditional Probability MeasureDependent Evolution Equations, Inverse Problems, 32(9), 095005, September 2016. doi arXiv
 D.D. Keck & D.M. Bortz. Generalized sensitivity functions for sizestructured population models, Journal of Inverse and Illposed Problems, 24(3), 309321, June 2016. doi arXiv
 J.T. Nardini, D.A. Chapnick, X. Liu, D.M. Bortz. Modeling Keratinocyte Wound Healing Dynamics: Cellcell Adhesion Promotes Sustained Collective Migration, Journal of Theoretical Biology, 400(July), 103117, 2016. doi. arXiv
 J.A. Stotsky, J.F. Hammond, L. Pavlovsky, E.J. Stewart, J.G. Younger, M.J. Solomon, D.M. Bortz. Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part II: Experimental Validation and the Heterogeneous RheologyIBM, Journal of Computational Physics, 317(July), 204222, 2016 doi. arXiv
 D.M. Bortz. Eigenvalues for a Twolag linear delay differential equation, IFACPapersOnline, 48(12):13–16, 2015 doi
 I. Mirzaev & D.M. Bortz. Laplacian Dynamics with Synthesis and Degradation, Bulletin of Mathematical Biology 2015 doi arXiv.
 D.M. Bortz. Chapter 17: Modeling and simulation for nanomaterials in fluids: Nanoparticle selfassembly. In V. Tewary & Y. Zhang, editors, Modeling, characterization, and production of nanomaterials (Electronics, Photonics and Energy applications), 419441, Woodhead/Elsevier, 2015.
 S. Sircar, E. Aisenbrey, S. Bryant & D.M. Bortz, Determining average osmolarity in Poly(ethylene glycol)Chondrotin sulfate gels mimicking cartillage. Journal of Theoretical Biology 364(Jan), 394406, 2015. doi arXiv
 S. Sircar, J. G. Younger, & D.M. Bortz. Sticky surface: sphere–sphere adhesion dynamics. Journal of Biological Dynamics 2014 doi arXiv
 S.M. Kissler, C. Cichowitz, S. Sankaranarayanan, & D.M. Bortz. Determination of personalized diabetes treatment plans using a twodelay model. Journal of Theoretical Biology, 359(Oct), 101111, 2014 doi arXiv
 J. F. Hammond, E. J. Stewart, M. J. Solomon, J. G. Younger, & D.M. Bortz. Variable viscosity and density biofilm simulations using an Immersed Boundary Method, Part I: numerical scheme and convergence results. Computer Modeling in Engineering & Sciences, 98(3), 295340, 2014 doi arXiv (Invited paper as a part of a special issue on Computational Mechanobiology and Soft Matter Mechanics.)
 G. Lambert, A. Bergman, Q. Zhang, D.M. Bortz, & R. Austin. Physics of Biofilms: The Initial Stages of Biofilm Formation and Dynamics. New J. Physics, 16(4), 045005, Apr. 2014. doi
 S. Sircar & D.M. Bortz. Impact of flow on ligandmediated bacterial flocculation. Mathematical Biosciences, 245(2), 314321, Oct. 2013. doi
 A. Satorius, J. Szafranski, A. Rivera, D. Pynes, M. Ghanesan, M. J. Solomon, D. Newton, D.M. Bortz, & J. G. Younger, Complement C5a Generation by Staphylococcus epidermidis Biofilms. SHOCK, 39(4), 336342, Apr. 2013. doi
 E. C. Conrad, Y.Y. Hsu, D.M. Bortz, & J. G. Younger. Spatiotemporal Dynamics of Complement C5a Production within Bacterial Extracellular Polymeric Substance. Journal of Innate Immunity, 5, 114123, Jan. 2013. (cover art!). doi
 C. W. Curtis & D.M. Bortz, Propagation of fronts in the FisherKolmogorov equation with quadratically varying diffusion. Phys. Rev. E, 86(6), 066108, Dec. 2012. doi arXiv
 M. Thornton, C. Irvin, H. M. Chung, D.M. Bortz, M. J. Solomon, & J. G. Younger, Multicellularity and Antibiotic Resistance in Klebsiella pneumoniae Grown under BloodstreamMimicking Fluid Dynamic Conditions. Journal of Infectious Diseases, 206(4), 588595, Aug. 2012. doi:10.1093/infdis/jis397
 J. F. Hammond & D.M. Bortz, Analytical solutions to Fisher’s equation with timevariable coefficients. Applied Mathematics and Computation, 218(6), 24972508, 2011. doi:10.1016/j.amc.2011.03.163
 E. C. Byrne, S. Dzul, M. J. Solomon, J. G. Younger, & D.M. Bortz, Postfragmentation density function for bacterial aggregates in laminar flow. Phys. Rev. E, 83(4), 41911, 2011. doi:10.1103/PhysRevE.83.041911
 S. P. Dzul, M. M. Thornton, D. N. Hohne, E. J. Stewart, A. A. Shah, D.M. Bortz, M. J. Solomon, and J. G. Younger. Contribution of the Klebsiella pneumoniae Capsule to Bacterial Aggregate and Biofilm Microstructures. Applied Environmental Microbiology, 77(5):1777–1782, Mar. 2011. doi:10.1128/AEM.0175210
 C. M. Nypaver, M. M. Thornton, S. M. Yin, D. O. Bracho, P. W. Nelson, A. E. Jones, D.M. Bortz, & J. G. Younger, Dynamics of Human Complement―Mediated Killing of Klebsiella pneumoniae, American journal of respiratory cell and molecular biology, 43(5), 585590, 2010. doi:10.1165/rcmb.20090292OC
 H. Chung, M. M. Cartwright, D.M. Bortz, T. L. Jackson, & J. G. Younger, Dynamical System Analysis of Staphylococcus epidermidis Bloodstream Infection, SHOCK, 30(5):518526, November 2008. doi:10.1097/SHK.0b013e31816a0b77 (cover art!)
 D.M. Bortz, T. L. Jackson, K. A. Taylor, A. P. Thompson, & J. G. Younger, Klebsiella pneumoniae flocculation dynamics, Bulletin of Mathematical Biology, 70(3):745768, April 2008. doi:10.1007/s115380079277y
 D.M. Bortz & P. W. Nelson, Model selection and mixedeffects modeling of HIV infection dynamics, Bulletin of Mathematical Biology, 68(8):20052025, November 2006. doi:10.1007/s115380069084x
 S. Ciupe, B. L. Bivort, D.M. Bortz, & P. W. Nelson, Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Mathematical Biosciences, 200(1):127, March 2006. doi:10.1016/j.mbs.2005.12.006
 I. BenDavid, S. E. Price, D.M. Bortz, S. Cohen, A. L. Bauer, T. L. Jackson, & J. G. Younger, Dynamics of intrapulmonary bacterial growth in a murine model of repeated microaspirations, Am. J. Respiratory Cell & Molecular Biology, 33(5):476482, November 2005. doi:10.1165/rcmb.20050053OC
 H. T. Banks & D.M. Bortz, A parameter sensitivity methodology in the context of HIV delay equation models, Journal of Mathematical Biology, 50(6):607625, June 2005. doi:10.1007/s002850040299x
 H. T. Banks & D.M. Bortz, Inverse Problems for a Class of Measure Dependent Dynamical Systems, Journal of Inverse and Illposed Problems, 13(2):103121, April 2005. doi:10.1515/1569394053978515
 D.M. Bortz & P. W. Nelson, Sensitivity analysis of nonlinear lumped parameter models of HIV infection dynamics, Bulletin of Mathematical Biology, 66(5):10091026, September 2004. doi:10.1016/j.bulm.2003.10.011
 H. T. Banks, D.M. Bortz, G. A. Pinter, & L. K. Potter, Chapter 6: Modeling and imaging techniques with potential for applications in bioterrorism. In H. T. Banks and C. CastilloChavez, editors, Bioterrorism: Mathematical Modeling Applications in Homeland Security, volume 28 of Frontiers in Applied Mathematics, pages 129154, SIAM, Phildelphia, PA, 2003.
 H. T. Banks, D.M. Bortz, & S. E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Mathematical Biosciences, 183(1):6391, May 2003. doi:10.1016/S00255564(02)002183
 D.M. Bortz, A. D. Rubio, H. T. Banks, A. B. Cain, & R. C. Smith, Control of open bay acoustics by harmonic mass injection, International Journal of Aeroacoustics, 1(1), 6581, March 2002. doi:10.1260/1475472021502677
 A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith, Reduced Order Modeling in Control of Open Cavity Acoustics, Proceedings of the AIAA, AIAA20001928, June 2000.
 D.M. Bortz & C. T. Kelley, The simplex gradient and noisy optimization problems. In J. T. Borggaard, J. Burns, E. Cliff, and S. Schreck, editors, Computational Methods in Optimal Design and Control, volume 24 of Progress in Systems and Control Theory, Birkhauser, 1998, pp. 7790.
 I. Ambats, D.M. Bortz, A. Connolly, A. Derlicki, M. Derrick, W. Kahle, & J. Thron, Studies of HadronElectron Separators for the ZEUS Barrel Calorimeter, Nuclear Instruments and Methods in Physics Research Section A, 368(2), 364377, 1996. doi:10.1016/01689002(95)006214
Other Publications
 T. Kushner, D.M. Bortz, D. Maahs, and S. Sankaranarayanan, A DataDriven Approach to Artificial Pancreas Verification and Synthesis. In Intl. Conference on CyberPhysical Systems (ICCPS'18), pp. tba (2018). Note: To Appear
 I. Mirzaev & D.M. Bortz. Criteria for linearized stability for a sizestructured population model. arXiv:1502.02754
 E. C. Conrad, A. E. Satorius, P. Sharma, D.M. Bortz, & J. G. Younger. The Host Response to Line Sepsis: Experimental and Computational Analysis of Complement Activation against CoagulaseNegative Staphylococcal Biofilms. Annals of Emergency Medicine, 62(4):S153, 2013.
 J. G. Younger, M. M. Thornton, C. Babcock, H. M. ChungEsaki, D.M. Bortz, & M. J. Solomon. Bloodstreamlike fluid dynamic conditions promote multicellularity and antibiotic resistance in in Klebsiella pneumoniae. SHOCK, 37(1):58, 2012.
 D.M. Bortz & A. J. Christlieb. Scandalously Parallelizable Mesh Generation. arXiv:1103.5268
 M. M. Thornton, D. N. Hohne, M. J. Solomon, D.M. Bortz, & J. G. Younger. Bacterial aggregation during growth under low shear: implications for bacteremia. SHOCK, 31(7):22, 2009.
 D.M. Bortz & A. J. Christlieb. Random numerical discretizations. In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 29–30, 2008.
 D. Li, D. Hohne, D.M. Bortz, J. Bull, & J. G. Younger Modeling bacterial clearance from the bloodstream using computational fluid dynamics and monte carlo simulation. J. Critical Care, 22(4):344, Dec. 2007.
 J. G. Younger, H. Y. Chung, M. Cartwright, D.M. Bortz, & T. L. Jackson, Neutropenic Sepidermidis bacteremia modeled as a pharmacodynamic system, SHOCK, 27(Supplement 1):6869, June 2007.
 D.M. Bortz. Accurate model selection computations. J. Critical Care, 21(4):359, Dec. 2006.
 H. Chung, T. L. Jackson, D.M. Bortz, M. Cartwright, & J. G. Younger, Multiplecompartment bacterial clearance kinetics during murine bacteremia, Journal of Critical Care, 21(4):359360, December 2006.
 D.M. Bortz, T. L. Jackson, & J. G. Younger, Estimation and identification of Klebsiella pneumoniae flocculation dynamics, In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 1517, 2006.
 J. G. Younger, K. Taylor, A. Thompson, & D.M. Bortz. Quantification and modeling of aggregate bacterial growth in suspension: Implications for bacteremia. SHOCK, pages 79–80, June 2006.
 I. BenDavid, S. E. Price, S. Cohen, D.M. Bortz, T. L. Jackson, & J. G. Younger, Complement C3 is necessary for early suppression of intrapulmonary bacterial growth, SHOCK, 23(Supplement 3):7980, June 2005.
 A. L. Bauer, D.M. Bortz, D. Gammack, I. BenDavid, A. Stein, T. L. Jackson, & J. G. Younger, Virulence of Klebsiella pneumoniae predicted by nonlinear biodistributive mathematical model, SHOCK, 21(Supplement 2):29,2004.
 D.M. Bortz, Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations, Ph.D. dissertation, North Carolina State University, Raleigh, NC, 2002.
 D.M. Bortz, R. Guy, J. Hood, K. Kirkpatrick, V. Nguyen, & V. Shimanovich, Modeling HIV infection dynamics using delay equations, In P. A. Gremaud, Z. Li, R. C. Smith, and H. T. Tran, editors, Proceedings of the 2000 Industrial Mathematics Modeling Workshop for Graduate Students, pages 4858. Technical Report CRSCTR0024, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October 2000.
 A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith, Optimizing control of open bay acoustics, Tech. Report CRSCTR0009, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May 2000.
 A. S. Bondarenko, D.M. Bortz, & J. J. Moré, COPS: Largescale nonlinearly constrained optimization problems, Tech. Report ANL/MCSTM237, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, September 1998, revised October 1999.
 P. Barnes, D.M. Bortz, S. Frank, I. Loladze, E. Packard, & M. Santhanam, Power transformer clearance checking, In F. Reitich, J. S. Scroggs, and H. T. Tran, editors, Proceedings of the 1997 Industrial Mathematics Modeling Workshop for Graduate Students. Technical Report CRSCTR9809, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, February, 1998.
Funding
Group Alumni
(postgroup activities in parentheses, if known)
Other Useful Information
General List of fellowships
List at SIAM
List at CU
Fellowships/Awards for Graduate Students
NSF Graduate Fellowship Program
NSF Summer Internship Program
DOE Computational Science Graduate Fellowship
DOE Office of Science Graduate Student Research (SCGSR) Program
Center for Nonlinear Studies Summer Student Program
DOD Science and Engineering Graduate Fellowship
NIH Individual Predoctoral Fellowship
Science, Mathematics And Research for Transformation (SMART) Scholarship for Service Program
NASA Earth and Space Science Fellowship
GEM Fellowship Program
Hertz Foundation Graduate Fellowship
Ford Foundation Fellowship Program
GatesCambridge Fellowship
Google PHD Fellowships
NVIDIA Graduate Fellowships
Intel PHD Fellowship Program
IBM PHD Fellowship
Microsoft PhD Fellowship Program
Chateaubriand Fellowship
Soros Fellowships for New Americans
National Physical Science Consortium Fellowship
AAUW
HHMI fellowship for international students
SIAM student paper award
APS best dissertation awards
Fellowships for Postdocs
University of Colorado Chancellor's Postdoctoral Fellowship Program
BWF CASI
L'Oreal For Women in Science fellowship program
NIH F32 postdoctoral fellowship
NSF math postdoc
Life Sciences Research Foundation postdoc
NRC Research Associateship (deadlines)
JSMF Fellowship
USGS Postdoc
Fullbright Postdoc
AMSSimons Travel Grant
List of Free Math Books and Course Notes
American Mathematical Society Open Math Notes
American Institute of Mathematics Open Textbook Initiative
