Rachael Miller Neilan

Associate Professor, Assistant Chair
McAnulty College and Graduate School of Liberal Arts
Mathematics and Computer Science

College Hall 403A
Phone: 412.396.6477


Ph.D., Mathematics, The University of Tennessee, 2009
M.S., Mathematics, The University of Tennessee, 2007
B.S., Mathematics, Drexel University, 2004
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 
Math 415W - Real Analysis I
Math 416W - Real Analysis II
CPMA 518 - Vector Calculus (graduate-level)

My research is agent-based modeling and optimal control theory with applications in neuroscience, ecology, epidemiology, business, and oceanography.  Below is a brief description of my recent research projects.

Modeling neurons in the amygdala and their response to pain.  Agent-based models (ABMs) are stochastic simulation models that replicate the dynamics of a population by simulating the attributes and interactions of its individuals and the environment.  Currently, I am working with Dr. Ben Kolber and his lab to develop an ABM of the neurons in the amygdala and changes in their firing rates during painful stimulation.  Parameters in the model are estimated from the results of experiments measuring neural activity in mice during painful bladder stimulation.  The calibrated ABM results outputs the cumulative activity of neurons across the amygdala during painful events and is used to predict the development chronic pain over time.   

Assessment of environmental and managerial policies using complex computational models.   In 2011, I collaborated with ecologists to construct an agent-based model (ABM) for a mink population to evaluate the health of the population during exposure to polychlorinated biphenyls (PCBs) at a Superfund site. The model was used to assess the impact that different environmental clean-up strategies had on mink population endpoints. In 2015, an undergraduate student and I developed a spatial ABM for a feral cat population and included the use of trap-neuter-return (TNR) and trap-vasectomy-hysterectomy-return (TVHR) in the model as means of controlling population growth. Analysis of model simulations provided an understanding of when and where to apply TNR and TVHR and how many cats must be targeted to achieve effective control.

Predicting the effect of hypoxia on aquatic organisms. Hypoxia occurs when the oxygen in water is low enough to cause harmful effects on inhabiting organisms. I work with oceanographers to understand how intermittent hypoxic exposures affect fish and shrimp in the Gulf of Mexico. In 2014, we developed a mathematical model relating hourly hypoxic exposures to reductions in growth, survival, and reproductive ability of various aquatic species. This mathematical model was then embedded in a large-scale computational model simulating fish populations in the Gulf of Mexico. We are currently using these models to predict long-term effects of developing dead zones (hypoxic areas) in the Gulf of Mexico.

Mitigating disease spread with mathematical models and control theory. In 2013, a graduate student and I modeled the transmission of antibiotic-resistant bacteria in hospital intensive care units with a system of coupled differential equations. We applied optimal control theory to the model to determine cost-effect strategies combining quarantine and drug treatment options to reduce patient death.

Theoretical framework for optimization of agent-based models. Because agent-based models (ABMs) are complex computational models, they are not amenable to standard optimization techniques. Since 2011 I have been working with a group of researchers at NIMBioS, a national mathematics institute, to develop a theoretical framework for constructing optimal controls for ABMs. We have published two papers with examples of our approach and an overview of challenges in this area.


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).

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).

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) https://doi.org/10.1007/s10588-019-09295-4.

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. 

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) doi: 10.1007/s12237-017-0266-6.

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) doi: 10.1007/s12237-017-0267-5.

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.

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.

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.

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.

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.

R. Miller Neilan. Modeling fish growth in low dissolved oxygen, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies 23 (2013) 748 - 758.

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.

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.

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.

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.

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.

* Student co-author

Honors and Awards

The Council on Undergraduate Research Math/CS Division Faculty Mentor Award, 2020.

McAnulty College of Liberal Arts Excellence in Teaching Award, 2020.

Mathematical Association of America Allegheny Mountain Section Faculty Mentor Award, 2020. 

John G. Rangos Prize Award, 2019.

McAnulty College of Liberal Arts Junior Excellence in Teaching Award, 2017.

Duquesne University Lilly Fellow, 2014 - 2015.

MAA Project NExT Fellow, 2011 - 2012.