September 20, 2018, Thursday
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D M Bortz

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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 top-tier graduate programs (Berkeley, Caltech, Cambridge, Northwestern, Arizona, etc.) as well as ended up in positions at research-oriented (U. Minnesota, SAMSI, U. Adelaide, Air Force Research Lab) and teaching-oriented (Harvey Mudd, Olin College, Air Force Academy) institutions and in industry (Mathworks). They have also won several national and international awards, e.g., NSF-GRFP (4), DOE-CSGF (1), DOD-NDSEG (1), and Gates-Cambridge 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 (7/2018) I have no postdoctoral positions available.


  • Note that I check my email once a day, typically in the early morning. For time-sensitive issues, please call the main Applied Math office at (303) 492-4668 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 80309-0526

Students (support in parenthesis)





  1. K.A. Moore, S. Altus, J.W. Tay, J. Fox, E.B. Johnson, D.M. Bortz & J.C. Cameron, Mechanical Regulation of Photosynthesis, (submitted)
  2. J.T. Nardini & D.M. Bortz, The Influence of Numerical Error on an Inverse Problem Methodology in PDE Models, (submitted) arXiv
  3. J.A. Stotskky & D.M. Bortz, A Posteriori Error Analysis of Fluid-Stucture Interactions: Time Dependent Error, arXiv
  4. I. Mirzaev & D.M. Bortz. On the existence of non-trivial steady-state size-distributions for a class of flocculation equations, (submitted). arXiv
  5. 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
  6. S.H. Friedman, A.R.A. Anderson, D.M. Bortz, et al. MultiCellDS: A standard and a community for sharing multicellular data, (submitted). bioRxiv
  7. S.H. Friedman, A.R.A. Anderson, D.M. Bortz, et al. MultiCellDS: a community-developed standard for curating microenvironment-dependent multicellular data, (submitted). bioRxiv

Refereed Articles & Book Chapters

  1. J.M. Wentz, A.R. Mendenhall, & D.M. Bortz. Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans, Bulletin of Mathematical Biology, (accepted). doi arXiv
  2. 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
  3. 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
  4. E.P. Kightley, A. Pearson, J.A. Evans, & D.M. Bortz. Fragmentation of biofilm-seeded bacterial aggregates in shear flow, Eur. J. Appl. Math., (accepted). doi arXiv
  5. V. Dukic & D.M. Bortz, Uncertainty Quantification Using Probabilistic Numerics: Application to Models in Mathematical Epidemiology, Inverse Problems in Science and Engineering, 28(2):223-232, 2018 doi.
  6. I. Mirzaev & D.M. Bortz. A numerical framework for computing steady states of size-structured population models and their stability, Mathematical Biosciences and Engineering, 14(4):933-952, 2017. doi arXiv.
  7. D.M. Bortz, Characteristic roots for two-lag linear delay differential equations, Discrete and Continuous Dynamical System - B, 21(8):2409-2422, Oct. 2016 doi.
  8. I. Mirzaev, E.C. Byrne, & D.M. Bortz. An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations, Inverse Problems, 32(9), 095005, September 2016. doi arXiv
  9. D.D. Keck & D.M. Bortz. Generalized sensitivity functions for size-structured population models, Journal of Inverse and Ill-posed Problems, 24(3), 309-321, June 2016. doi arXiv
  10. J.T. Nardini, D.A. Chapnick, X. Liu, D.M. Bortz. Modeling Keratinocyte Wound Healing Dynamics: Cell-cell Adhesion Promotes Sustained Collective Migration, Journal of Theoretical Biology, 400(July), 103-117, 2016. doi. arXiv
  11. 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 Rheology-IBM, Journal of Computational Physics, 317(July), 204-222, 2016 doi. arXiv
  12. D.M. Bortz. Eigenvalues for a Two-lag linear delay differential equation, IFAC-PapersOnline, 48(12):13–16, 2015 doi
  13. I. Mirzaev & D.M. Bortz. Laplacian Dynamics with Synthesis and Degradation, Bulletin of Mathematical Biology, 77(6):1013-1045, 2015. doi arXiv
  14. D.M. Bortz. Chapter 17: Modeling and simulation for nanomaterials in fluids: Nanoparticle self-assembly. In V. Tewary & Y. Zhang, editors, Modeling, characterization, and production of nanomaterials (Electronics, Photonics and Energy applications), 419-441, Woodhead/Elsevier, 2015.
  15. 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), 394-406, 2015. doi arXiv
  16. S. Sircar, J. G. Younger, & D.M. Bortz. Sticky surface: sphere–sphere adhesion dynamics. Journal of Biological Dynamics 2014 doi arXiv
  17. S.M. Kissler, C. Cichowitz, S. Sankaranarayanan, & D.M. Bortz. Determination of personalized diabetes treatment plans using a two-delay model. Journal of Theoretical Biology, 359(Oct), 101-111, 2014 doi arXiv
  18. 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), 295-340, 2014 doi arXiv (Invited paper as a part of a special issue on Computational Mechanobiology and Soft Matter Mechanics.)
  19. 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
  20. S. Sircar & D.M. Bortz. Impact of flow on ligand-mediated bacterial flocculation. Mathematical Biosciences, 245(2), 314-321, Oct. 2013. doi
  21. 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), 336-342, Apr. 2013. doi
  22. 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, 114-123, Jan. 2013. (cover art!). doi
  23. C. W. Curtis & D.M. Bortz, Propagation of fronts in the Fisher-Kolmogorov equation with quadratically varying diffusion. Phys. Rev. E, 86(6), 066108, Dec. 2012. doi arXiv
  24. 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 Bloodstream-Mimicking Fluid Dynamic Conditions. Journal of Infectious Diseases, 206(4), 588-595, Aug. 2012. doi:10.1093/infdis/jis397
  25. J. F. Hammond & D.M. Bortz, Analytical solutions to Fisher’s equation with time-variable coefficients. Applied Mathematics and Computation, 218(6), 2497-2508, 2011. doi:10.1016/j.amc.2011.03.163
  26. 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
  27. 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.01752-10
  28. 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), 585-590, 2010. doi:10.1165/rcmb.2009-0292OC
  29. 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):518-526, November 2008. doi:10.1097/SHK.0b013e31816a0b77 (cover art!)
  30. 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):745-768, April 2008. doi:10.1007/s11538-007-9277-y
  31. D.M. Bortz & P. W. Nelson, Model selection and mixed-effects modeling of HIV infection dynamics, Bulletin of Mathematical Biology, 68(8):2005-2025, November 2006. doi:10.1007/s11538-006-9084-x
  32. 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):1-27, March 2006. doi:10.1016/j.mbs.2005.12.006
  33. I. Ben-David, 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):476-482, November 2005. doi:10.1165/rcmb.2005-0053OC
  34. H. T. Banks & D.M. Bortz, A parameter sensitivity methodology in the context of HIV delay equation models, Journal of Mathematical Biology, 50(6):607-625, June 2005. doi:10.1007/s00285-004-0299-x
  35. H. T. Banks & D.M. Bortz, Inverse Problems for a Class of Measure Dependent Dynamical Systems, Journal of Inverse and Ill-posed Problems, 13(2):103-121, April 2005. doi:10.1515/1569394053978515
  36. D.M. Bortz & P. W. Nelson, Sensitivity analysis of nonlinear lumped parameter models of HIV infection dynamics, Bulletin of Mathematical Biology, 66(5):1009-1026, September 2004. doi:10.1016/j.bulm.2003.10.011
  37. 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. Castillo-Chavez, editors, Bioterrorism: Mathematical Modeling Applications in Homeland Security, volume 28 of Frontiers in Applied Mathematics, pages 129-154, SIAM, Phildelphia, PA, 2003.
  38. 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):63-91, May 2003. doi:10.1016/S0025-5564(02)00218-3
  39. 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), 65-81, March 2002. doi:10.1260/1475472021502677
  40. 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, AIAA-2000-1928, June 2000.
  41. 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. 77-90.
  42. I. Ambats, D.M. Bortz, A. Connolly, A. Derlicki, M. Derrick, W. Kahle, & J. Thron, Studies of Hadron-Electron Separators for the ZEUS Barrel Calorimeter, Nuclear Instruments and Methods in Physics Research Section A, 368(2), 364-377, 1996. doi:10.1016/0168-9002(95)00621-4

Other Publications

  1. T. Kushner, D.M. Bortz, D. Maahs, and S. Sankaranarayanan, A Data-Driven Approach to Artificial Pancreas Verification and Synthesis. In Intl. Conference on Cyber-Physical Systems (ICCPS'18), 242–52. ICCPS ’18. Porto, Portugal: IEEE Press, 2018.
  2. I. Mirzaev & D.M. Bortz. Criteria for linearized stability for a size-structured population model. arXiv:1502.02754
  3. 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 Coagulase-Negative Staphylococcal Biofilms. Annals of Emergency Medicine, 62(4):S153, 2013.
  4. J. G. Younger, M. M. Thornton, C. Babcock, H. M. Chung-Esaki, D.M. Bortz, & M. J. Solomon. Bloodstream-like fluid dynamic conditions promote multicellularity and antibiotic resistance in in Klebsiella pneumoniae. SHOCK, 37(1):58, 2012.
  5. D.M. Bortz & A. J. Christlieb. Scandalously Parallelizable Mesh Generation. arXiv:1103.5268
  6. 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.
  7. D.M. Bortz & A. J. Christlieb. Random numerical discretizations. In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 29–30, 2008.
  8. 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.
  9. J. G. Younger, H. Y. Chung, M. Cartwright, D.M. Bortz, & T. L. Jackson, Neutropenic S-epidermidis bacteremia modeled as a pharmacodynamic system, SHOCK, 27(Supplement 1):68-69, June 2007.
  10. D.M. Bortz. Accurate model selection computations. J. Critical Care, 21(4):359, Dec. 2006.
  11. H. Chung, T. L. Jackson, D.M. Bortz, M. Cartwright, & J. G. Younger, Multiple-compartment bacterial clearance kinetics during murine bacteremia, Journal of Critical Care, 21(4):359-360, December 2006.
  12. 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 15-17, 2006.
  13. 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.
  14. I. Ben-David, 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):79-80, June 2005.
  15. A. L. Bauer, D.M. Bortz, D. Gammack, I. Ben-David, A. Stein, T. L. Jackson, & J. G. Younger, Virulence of Klebsiella pneumoniae predicted by nonlinear biodistributive mathematical model, SHOCK, 21(Supplement 2):29,2004.
  16. 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.
  17. 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 48-58. Technical Report CRSC-TR00-24, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October 2000.
  18. A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith, Optimizing control of open bay acoustics, Tech. Report CRSC-TR00-09, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May 2000.
  19. A. S. Bondarenko, D.M. Bortz, & J. J. Moré, COPS: Large-scale nonlinearly constrained optimization problems, Tech. Report ANL/MCS-TM-237, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, September 1998, revised October 1999.
  20. 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 CRSC-TR98-09, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, February, 1998.


Group Alumni

(post-group 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

Gates-Cambridge 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


HHMI fellowship for international students

SIAM student paper award

APS best dissertation awards

Fellowships for Postdocs

University of Colorado Chancellor's Postdoctoral Fellowship Program


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

AMS-Simons Travel Grant

List of Free Math Books and Course Notes

American Mathematical Society Open Math Notes

American Institute of Mathematics Open Textbook Initiative