Benjamin Armbruster

Stanford PhD in Management Science and Engineering

email: [lastname][first initial]
office: Tech M237 (maps and directions)

Jump to papers, students, and previous teaching.

Research Interests

My research focuses on problems in healthcare and the mathematical tools to tackle them. Applications include policy problems such as determining the most cost-effective way to (a) identify cases, (b) treat cases, or (c) prevent cases of a disease. Often this related to modeling the spread of infectious diseases. Mathematical tools for such problems include deterministic and stochastic optimization and optimal control.

Healthcare Engineering at Northwestern


  • HIV tracing paper posted
  • HIV concurrency paper posted
  • Dynamic networks draft posted
  • HIV dissolution rates draft posted
  • Strassen's theorem draft posted
  • Robust utility draft posted

If you download a file, and we have never corresponded before, please send me a note. I like to know who is interested. For the website, I've scaled the posters to letter paper size.

Health Policy

Forward Reachable Sets: Analytically derived properties of connected components for dynamic networks with Li Wang and Martina Morris, draft.

Optimal timing of cross-sectional network samples in longitudinal network studies with Ekkehard Beck, draft.

Population and dyadic-based seroincidence of herpes simplex virus-2 and syphilis in southern India Sex Transm Infect 2015;91:375-382, with Chad H Hochberg, John A Schneider, Rakhi Dandona, Vemu Lakshmi, G Anil Kumar, Talasila Sudha, Mohammed Akbar, G Md Mushtaq Ahmed, Sri P Ramgopal, Michel Alary, and Lalit Dandona.

A simple and general proof for the convergence of Markov processes to their mean-field limits draft.

Implications of Switching Away From Injectable Hormonal Contraceptives on the HIV epidemic, Socio-Economic Planning Sciences Vol 52 (2015) December, 1-9, with Kezban Yagci Sokat.

Elementary proof of convergence to the mean-field model for the SIR process [journal page] Journal of Mathematical Biology, with Ekkehard Beck. In press.

A data-driven simulation of HIV spread among young men who have sex with men: role of age and race mixing and STIs [supplement] JAIDS 2015; 70(2):186-194, with Ekkehard Beck, Michelle Birkett, and Brian Mustanski.

Bounds for the expected value of one-step processes Communications in Mathematical Sciences (2016) 14(7):1911-1923, with Ádám Besenyei, Péter L. Simon.

An elementary proof of convergence to the mean-field equations for an epidemic model IMA Journal of Applied Mathematics (2016), with Ekkehard Beck.

Social Networks and Text Messaging in Public Health [pdf] Northwestern Public Health Review vol. 2, issue 1 (2014), with Ekkehard Beck.

Sex Role Segregation and Mixing among Men Who Have Sex with Men: Implications for Biomedical HIV Prevention Interventions PLoS ONE 8(8): e70043, with Sourya Roy, Abhinav Kapur, and John A. Schneider.

The Importance of Extended High Viremics in Models of HIV Spread in South Africa accepted to Health Care Management Science, with Ekkehard Beck and Mustafa Waheed.

The cost-effectiveness of expanded HIV screening in the United States [Supplement] [journal page] AIDS 27 (2013) 795-801, with Aaron Lucas. One of two featured articles in that issue. Press: Northwestern press release, Take Part, and Prevention Magazine.

Speeding Up Network Simulations Using Discrete Time draft, with Aaron Lucas.

Effectiveness of a no-sex or safe-sex month in reducing HIV transmission Bulletin of the World Health Organization 90 (2012) 477-556, with Aaron Lucas.

Exploring the relative costs of contact tracing in increasing HIV case-finding in sub-Saharan countries: the case of Likoma Island (Malawi) JAIDS 58 (2011) 29-36, with Stephane Helleringer, Hans-Peter Kohler, Linda Kalilani-Phiri, and James Mkandawire.

HIV Status Awareness, Partnership Dissolution and HIV Transmission in Generalized Epidemics PLoS ONE 7(12): e50669, with Georges Reniers. preprint

The reliability of sexual partnership histories: implications for the measurement of partnership concurrency during surveys AIDS 25 (2011) 503-511, with Stephane Helleringer, Hans-Peter Kohler, Linda Kalilani-Phiri, and James Mkandawire.

Two Additional Implications of an HIV Nucleic Acid Testing Program With Automated Internet and Voicemail Systems to Deliver Results Annals of Internal Medicine 153 (2010) 549 (letter).

Cost-Effective Control of Chronic Viral Diseases: Finding the Optimal Level of Screening and Contact Tracing Mathematical Biosciences 224 (2010) 35-42, with Margaret L. Brandeau.

The Cost-Effectiveness of Contact Tracing for Endemic Diseases a poster at the Operating on Health Care conference in UBC, August 16-17, 2007, with Margaret L. Brandeau.

Contact Tracing to Control Infectious Disease: When Enough is Enough Health Care Management Science 10 (2007) 341-355, with Margaret L. Brandeau.

Who Do You Know? A Simulation Study of Infectious Disease Control Through Contact Tracing with Margaret L. Brandeau; Proceedings of the 2007 International Conference on Health Sciences Simulation (ICHSS), part of the 2007 Western MultiConference on Modeling & Simulation (WMC). Here are the slides accompanying my talk.

Optimal mix of screening and contact tracing for endemic diseases Mathematical Biosciences 209 (2007) 386-402, with Margaret L. Brandeau. I gave a guest lecture about this work March 14, 2006 in MS&E 292 (accompanying slides). This script generates the figures using Matlab 7.

Medical Physics

Note that AAPM is the American Association of Physicists in Medicine and that ASTRO is the American Society for Therapeutic Radiology and Oncology.

Formulating Adaptive Radiation Therapy (ART) Treatment Planning into a Closed-Loop Control Framework Physics in Medicine and Biology 52 (2007) 4137-4153, with Adam de la Zerda and Lei Xing. We presented a poster at the 2006 AAPM meeting on this work.

Dynamic Segment-Based Optimization (SBO) for 4D IMRT, a poster for the 2006 AAPM meeting with Adam de la Zerda and Lei Xing.

Spectrum Reconstruction from Dose Measurements as a Linear Inverse Problem Physics in Medicine and Biology 49 (2004) 5087-5099, with Russell J. Hamilton and Arthur K. Kuehl.

Mathematical Programming Formulations for Optimizing Radiation Treatment Strategies Proceedings of the 2004 IIE Annual Conference, with Russell J. Hamilton, Martin E. Lachaine, and J. Cole Smith. Here are the slides accompanying my talk. IIE is the Institute of Industrial Engineers.

Other Papers

Decision Making under Uncertainty when Preference Information is Incomplete Management Science 61 (2015) 111-128, with Erick Delage.

A Short Proof of Strassen's Theorem draft.

Dynamic Network Models draft, with John Gunnar Carlsson.

A bottleneck matching problem with edge-crossing constraints International Journal of Computational Geometry and Applications Vol 25 No 4 (2015) 245-261, with John Gunnar Carlsson, Saladi Rahul, and Haritha Bellam.

Multivariate Dominance Constrained Stochastic Programs IIE Transactions 47 (2015) 1-14, with James Luedtke.

Equilibrium in Prediction Markets with Buyers and Sellers Economics Letters 109 (2010) 46-49, with Shipra Agrawal and Nimrod Megiddo, also available as an IBM research report.

Dynamic Spectrum Management with the Competitive Market Model IEEE Transactions on Signal Processing 58 (2010) 2442-2446, with Yao Xie and Yinyu Ye.

Finding Equitable Convex Partitions of Points in a Polygon Efficiently ACM Transactions on Algorithms 6 (2010) Article 72, with John Gunnar Carlsson and Yinyu Ye. Here are some slides illustrating the heart of the algorithm. examples code

Finding 2d ham sandwich cuts in linear time draft (comments encouraged).

Sample Complexity of Smooth Stochastic Optimization draft (comments encouraged). I gave a guest lecture on this subject on March 9, 2006 in the MS&E INFORMS seminar (accompanying slides).

A Packet Filter Placement Problem with Application to Defense Against Spoofed Denial of Service Attacks European Journal of Operational Research 176 (2007) 1283-1292, with J. Cole Smith and Kihong Park

Fast Accurate Simulation of Physical Flows in Demand Networks Proceedings of the 2001 Semiconductor Manufacturing Operational Modeling and Simulation Symposium (SMOMS), with Karl G. Kempf, John W. Fowler, Kraig Knutson, Praveen Babu, and Brett M. Duarte.

Links to Coauthors

Shipra Agrawal, Ekkehard Beck, Michelle A. Birkett, Brian Mustanski, Ádám Besenyei, Margaret L. Brandeau (adviser), John Gunnar Carlsson, Erick Delage, John W. Fowler, Russell J. Hamilton, Stephane Helleringer, Karl G. Kempf, Hans-Peter Kohler, Martin E. Lachaine, Aaron Lucas, James Luedtke, Nimrod Megiddo, Kihong Park, Saladi Rahul, Georges Reniers, John Schneider, Péter L. Simon, J. Cole Smith, Yao Xie, Lei Xing, Kezban Yagci Sokat, and Yinyu Ye.


Aaron Lucas, Ekkehard Beck, and Kezban Yagci Sokat


IEMS 490: Health Policy Modeling Fall 2009

IEMS 443: Health Policy Modeling Fall 2012, Fall 2011

IEMS 460-2: Stochastic Models II Spring 2014, Spring 2013, Spring 2012, Spring 2011

IEMS 326: Economics and Finance for Engineers Fall 2012, Fall 2011, Spring 2011, Winter 2011, Winter 2010, Winter 2009

IEMS 310: Operations Research Spring 2009

Stanford MS&E 444: Investment Practice (a finance project class) Spring 2008, Spring 2007


IEMS, CreditLab