Contact Information


Dr. Rachael Neilan is a Professor of Mathematics in the School of Science and Engineering at Duquesne University.  Dr. Neilan teaches undergraduate and master's level courses in mathematics and applied mathematics.  She received multiple school, regional, and national awards for her excellence in teaching and mentorship.  Dr. Neilan currently serves as the faculty director for the Applied Math B.S. program.

Dr. Neilan's research is in mathematical biology with a focus on agent-based modeling and optimal control theory. Her interdiscplinary research involves the development of computational and mathematical models to study population  dynamics in neuroscience, ecology, social sciences, and disease transmission.  She holds multiple NIH grants (R15, R01) focused on developing novel models of pain-related neural activity in the amygdala.   

Dr. Neilan has a long-standing history of including undergraduate and M.S. students in her research. All of her student researchers have presented their work at international, national, or regional conferences and many have won awards for their outstanding research contributions. Dr. Neilan frequently co-authors research publications with these students. 


Ph.D., Mathematics, The University of Tennessee, 2009
M.S., Mathematics, The University of Tennessee, 2007
B.S., Mathematics, Drexel University, 2004


Profile Information

  • The Council on Undergraduate Research (CUR) Math/CS Division Faculty Mentor Award, 2020.
  • McAnulty College of Liberal Arts Excellence in Teaching Award, 2020.
  • Mathematical Association of America (MAA) Allegheny Mountain Section Mentor Award, 2020.
  • McAnulty College of Liberal Arts Junior Excellence in Teaching Award, 2017.
  • Duquesne University Lilly Fellow, 2014 – 2015.
  • MAA Project NExT Fellow, 2011 – 2012.
MATH 100 Calculus with Algebra I
MATH 101  College Algebra
MATH 110  Calculus with Algebra II
MATH 135  Discrete Mathematics
MATH 115  Calculus I
MATH 116  Calculus II
MATH 314  Differential Equations
MATH 314-SL Differential Equations with service-learning
MATH 317-ACEL Mathematical Modeling (community-engaged course)
MATH 415W  Real Analysis I
MATH 481-ACEL Applied Math Capstone (community-engaged course)
DTSC 481-ACEL  Data Science Capstone (community-engaged course)
MATH 416W Real Analysis II
CPMA 518  Vector Calculus (graduate-level)
*Student co-author
  1. R. Miller Neilan, C. Reith*, I. Anandan*, K. Kraeuter*, H. Allen, and B. Kolber. Developing a 3-D computational model of neurons in the central amygdala to understand pharmacological targets for pain. Frontiers in Pain Research 4 (2023).  
  2. R. Miller Neilan, G. Majetic*, M. Gil-Silva, A. Adke, Y. Carrasquillo, and B. Kolber. Agent-based modeling of the central amygdala and pain using cell-type specific physiological parameters, PLoS Computational Biology 17 (2021).
  3. K. de Castro*, E. Donoso Brown, R. Miller Neilan, and S. Wallace. Feasibility of Using Commercially Available Accelerometers to Monitor Upper Extremity Home Practice With Persons Post-stroke: A Secondary Data Analysis, Frontiers in Virtual Reality 2 (2021).
  4. J. Di Pietrantonio*, R. Miller Neilan, and J. Schreiber. Assessing the impact of motivation and ability on team-based productivity using an agent-based model, Computational and Mathematical Organization Theory (2019).
  5. J. Baktay*, R. Miller Neilan, M. Behun*, N. McQuaid*, and B. Kolber.  Modeling Neural Behavior and Pain During Bladder Distention using an Agent-based Model of the Central Nucleus of the Amygdala, Spora: A Journal of Biomathematics: 5 (2019) 1- 13.
  6. K. Rose, S. Creekmore, P. Thomas, J.K. Craig, Md S. Rahman, R. Miller Neilan. Modeling the population effects of hypoxia on Atlantic croaker (Micropogonias undulatus) in the northwestern Gulf of Mexico: Part 1 - Model descriptions and idealized hypoxia, Estuaries and Coasts (2017).
  7. K. Rose, S. Creekmore, D. Justic, P. Thomas, J.K. Craig, R. Miller Neilan, L. Wang, Md S. Rahman, D. Kidwell. Modeling the population effects of hypoxia on Atlantic croaker (Micropogonias undulatus) in the northwestern Gulf of Mexico: Part 2 - Realistic hypoxia and eutrophication, Estuaries and Coasts (2017).
  8. B. Fitzpatrick, G. An, S. Christley, P. Federico, A. Kanarek, R. Miller Neilan, M. Oremland, R. Salinas, R. Laubenbacher, S. Lenhart. A systems view of agent-based models in biology, Bulletin of Mathematical Biology, 79 (2017) 63-87.
  9. T. Ireland* and R. Miller Neilan. A spatial agent-based model of feral cats and analysis of population and nuisance controls, Ecological Modelling 337 (2016) 123 - 136.
  10. S. Christley, R. Miller Neilan, M. Oremland, R. Salinas, S. Lenhart. Optimal control of the Sugarscape ABM via a PDE model, Optimal Control Applications and Methods (2016) doi: 10.1002/oca.2265.
  11. J. Lowden*, R. Miller Neilan, and M. Yahdi. Optimal control of vancomycin-resistant enterococci using preventive care and treatment of infections, Mathematical Biosciences 249 (2014) 8 - 17.
  12. R. Miller Neilan and K. A. Rose. Simulating the effects of fluctuating dissolved oxygen on growth, reproduction, and survival of fish and shrimp, Journal of Theoretical Biology 343 (2014) 54 - 68.
  13. R. Miller Neilan. Modeling fish growth in low dissolved oxygen, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies 23 (2013) 748 - 758.
  14. C.J. Salice, B. Sample, R. Miller Neilan, K.A. Rose, and S. Sable. Evaluation of alternative PCB clean-up strategies using an individual-based population model of mink, Environmental Pollution 159 (2011) 3334 - 3343.
  15. R. Miller Neilan and S. Lenhart. Optimal control applied to a spatiotemporal epidemic model with application to rabies and raccoons, Journal of Mathematical Analysis and Applications 378 (2011) 603 - 619.
  16. R. Miller Neilan, E. Schaefer, H. Gaff, K. Fister, and S. Lenhart. Modeling the spread of cholera and optimal intervention methods, Bulletin of Mathematical Biology 72 (2010) 2004 - 2018.
  17. R. Miller Neilan and S. Lenhart. An introduction to optimal control for disease models, in: A.B. Gumel and S. Lenhart (Eds.), Modeling Paradigms and Analysis of Disease Transmission Models, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Rhode Island, 2010, pp. 67 - 81.
  18. D. Kern, S. Lenhart, R. Miller Neilan, and J. Yong. Optimal control applied to native-invasive population dynamics, Journal of Biological Dynamics 1 (2007) 413 - 426.
Research Grants
National Institutes of Health (NIH) 2 R01 DK115478}, 2023 -- 2028. Impact of amygdala lateralization on processing and modulation of bladder pain. PI: B. Kolber, Co-Is: R. Miller Neilan, J. Ploski.

National Institutes of Health (NIH) R15 NS128624, 2023 -- 2026. The integration of laboratory data with computational 3-D modeling to analyze the role of the central amygdala in neuropathic pain.  PI: R. Miller Neilan, Co-I: B. Kolber. 

Duquesne University Faculty Development Fund, 2022 -- 2024.  A 3-D computational model of pain-related neurons in the amygdala.  PI: R. Miller Neilan.

Chance to Change Lives (CCL-US) STEM Research Grant, 2022 -- 2023. A computational neuroscience approach to understanding pain.  PI: R. Miller Neilan.

National Institutes of Health (NIH) R01 DK115478, 2018 -- 2023. Impact of amygdala lateralization on processing and modulation of bladder pain. PI: B. Kolber, Co-I: R. Miller Neilan.

Association of Women in Mathematics (AWM) Travel Award, 2019 & 2015.

Duquesne University Faculty Development Fund, 2015 -- 2016.  A Mathematical Model for Feral Cat Colonies in Pittsburgh and Analysis of Optimal Cost-Effective TNR Policies.  PI: R. Miller Neilan. 
Duquesne University Presidential Scholarship Award, 2012 -- 2013. Mathematical Model for Growth, Reproduction, and Survival of Fish and Shrimp Exposed to Low Dissolved Oxygen.   PI: R. Miller Neilan.

Teaching Grants
Mathematical Association of America Preparing for Industrial Careers in Mathematics (PIC Math) Grant,  2021 -- 2022 & 2023 -- 2024. 

John G. Rangos Prize Award,  2019 -- 2020. Solving real-world problems using agent-based modeling.

Duquesne University McAnulty College of Liberal Arts NEH Endowment Fund, 2014 -- 2015.  Support for `Careers in Mathematics' Seminar Series

Duquesne University Service-Learning Award, 2013 -- 2014.  Development of Service Learning Course in Differential Equations

Grants to Support Women in STEM
Clare Booth Luce Foundation,  2021 -- 2024. Scholarship funding for undergraduate females in STEM majors. Co-PIs: R. Miller Neilan, J. Aitken, F. Benmokhtar, K. Williams.

Charles Henry Leach Fund, 2021 -- 2022. Summer research support for undergraduate females in STEM.  Co-PIs: R. Miller Neilan, J. Aitken, F. Benmokhtar, K. Williams.

EQT Foundation, 2018 -- 2022.  Promoting and supporting K-12 students and undergraduate females to pursue careers in science.  Co-PIs: R. Miller Neilan, J. Aitken, R. Harbourne, M. Heo, P. Ozturk, F. Benmokhtar, K. Williams.

Charles Henry Leach Fund, 2017 -- 2019. Support for STEM-related outreach activities.  Co-PIs: R. Miller Neilan, J. Aitken, R. Harbourne, M. Heo, P. Ozturk, F. Benmokhtar, K. Williams, A. O'Donnell.