Stephen J. Merrill

Professor Emeritus of Mathematics

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Major Research Interests

  • Mathematical models in immunology utilizing a variety of methods including differential equations and stochastic techniques
  • The role of randomness in dynamical systems
  • Creativity and dreaming
  • The mechanism of action of medicinal herbs
  • Cardiac Imaging
  • Atrial Fibrillation
  • Thyroid autoimmune disease and cancer
  • Malaria Control
  • The toxicology of novel compounds released from medical devices
  • Interactions of UV with HPV-associated cancer, melanoma, and other cancers

Education and Visiting Positions




NIH Reviewer 1984 (Immunology)

Selected to be a member in the 1st (1986) and 7th (1999) Bellman Prize Selection Committee Mathematical Biosciences (Elsevier)

NSF Reviewer 1988 (Prob. & Stat.)

NSF Reviewer 1989 (Prob. & Stat.)

NIH Reviewer 1989 (AIDS & Related Research)

NIH Site Visit 1990 (National Resource for Simulation)

NSF Reviewer 1990 (Prob. & Stat. and Applied Mathematics)

NIH Reviewer 1991 (Special Study Section)

Reviewer for Binational Science Foundation 1993 (US-Israel)

Reviewer for NSERC 1997 (Canada)

US Department of Education Spinal Cord Injury Centers Grant Review 2000, 2001

NIH Reviewer 2002, 2003 5 panels (Computational Biology)

NIH Reviewer 2004 2 panels (Modeling and Analysis of Biological Systems)

Marquette University Raynor Award for Teaching Excellence 2004

NIH Reviewer 2005 (Technology Development and Fellowship)

Reviewer for the Austrian Science Fund 2010 (Austria)

Reviewer for the Shota Rustaveli National Science Foundation -- Republic of Georgia 2011

Reviewer for the Binational Science Foundation 2011 (US-Israel)


Current and Recent Research

  • Modeling of the role of cofactors in an HIV infection ( this work has been reviewed in New Scientist 6 September, 1997, p. 12 : HIV's hidden helpers)
  • Markov chain analysis of heart rate variability and hypotensive events
  • Quantitative description of immune reconstitution after stem cell transplantation with St. Luke's Hospital in Milwaukee
  • Diversity in the HCV genome with the Blood Research Center in Milwaukee
  • Modeling of the microarray
  • Teaching the creative process
  • Modeling changes in the neurological exam with age
  • Cardiac imaging -3D information from a fluoroscopic image (patent)
  • UV and cancer of the throat and cervix (summarized (in Swedish) here)
  • Cutaneous Malignant Melanoma (CMM) incidence (reviewed here)
  • Thyroid autoimmunity (summarized in World Biomedical Frontiers)


Recent Talks, Abstracts, and Posters (Invited talk list)

Editorial Positions


  • Vladimir Brusic (Harvard) and Stephen J. Merrill were guest editors of a special issue of the Journal of Immunological Methods: High-throughput methods for immunology: Machine learning and automation

This is one of the first collections of papers in the new field of Immunomics, a subfield of Bioinformatics. This issue also reported the results of the machine learning competition on prediction of HLA class I binding peptides.


  • Salvatore Benvenga and Roberto Vita (U. of Messina, Italy) and Stephen J. Merrill edited a special issue of

Frontiers in Bioscience: Digging deep into thyroid pathophysiology which appeared in 2018-9. The issue involves papers in bioinformatics and mathematical models probing details of thyroid function.


       Balamurugan Pandiyan (UWW) and Stephen J. Merrill are editing a special issue of Mathematical Biosciences and Engineering: Mathematical Models and Autoimmune Diseases which will appear in 2019. This issue will contain models of aspects of autoimmunity and its connections to inflammation and cancer.


Most Recent Publications (Earlier Publications)

       S.J. Merrill, Computational Models in immunological methods: an historical review, J. Immunol. Meth., 126 (1998) 69-92.


  • J. Blimke, J. Myklebust, H. Volkmer, S. Merrill, Four-shell ellipsoidal model employing multipole expansion in ellipsoidal coordinates, Medical & Biological Engineering & Computing, 46 (2008) 859-869. doi:10.1007/s11517-008-0352-9
  • S.J. Merrill, The state of the science of nonlinear dynamics in 1963, Nonlinear Dynamics, Psychology and Life Sciences 13 (2009) 249-256.
  • Sheikh Iqbal Ahamed, Dennis Brylow, Rong Ge, Praveen Madiraju, Steve Merrill, Craig Struble, and Jim Early, Computational thinking in the sciences: A three day workshop for high school science teachers, In Proceedings of SIGCSE 2010: The 41st ACM Technical Symposium on Computer Science Education, pages 42-46, Milwaukee, Wisconsin, March 2010. doi:10.1145/1734263.1734277
  • S.J. Merrill, Markov Chains for identifying nonlinear dynamics, Chapter 17 in Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data, Stephen J. Guastello and Robert A.M. Gregson, eds., CRC Press, 2010, 401-423.
  • S. S. Kiware, N. Chitnis, S. J. Moore, G. J. Devine, S. Majambere, S. Merrill, and G. F. Killeen, Simplified models of vector control impact upon malaria transmission by zoophagic mosquitoes, PLoS ONE 7(5):e37661 (2012) doi:10.1371/journal.pone.0037661
  • B. Pandiyan, S.J. Merrill, and S. Benvenga, A patient-specific model of the negative-feedback control of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis, Mathematical Medicine and Biology 31(2013) 226-258. doi:10.1093/imammb/dqt005
  • R. Brown, S. White, J. Goode, P. Pradeep, and S.J. Merrill. Use of QSAR modeling to predict the carcinogenicity of color additives. Proceedings of the ASME/FDA 2013 1st Annual Frontiers in Medical Devices: Applications of Computer Modeling and Simulation. September 2013 doi:10.1115/FMD2013-16161
  • M. Adibuzzaman, G.C. Kramer, L. Galeotti, S.J. Merrill, D.G. Strauss, C.G. Scully, The mixing rate of the arterial blood pressure waveform Markov Chain is correlated with Shock Index during hemorrhage in anesthetized swine, Proceedings of Engineering in Medicine and Biology Society (EMBC), 2014 36th Annual International Conference of the IEEE, August 2014, 3268-3271. doi:10.1109/EMBC.2014.6944320
  • D.E. Godar, R. Tang, and S.J. Merrill, Pharyngeal and cervical cancer incidences significantly correlate with personal UV doses among whites in the United States, Anticancer Research 34: 4993-5000 (2014)
  • S.J. Merrill, S. Ashrafi, M. Subramanian, and D.E. Godar, Exponentially increasing incidences of cutaneous malignant melanoma in Europe correlate with low personal annual UV doses and suggests two major risk factors, Dermato-Endocrinology 7 (1): e1004018 (2015) doi:10.1080/19381980.2014.1004018
  • P. Pradeep, C. Struble, T. Neimman, D.S. Sem, and S.J. Merrill, A novel scoring based distributed protein docking application to improve enrichment, IEEE/ACM Transactions on Computational Biology and Bioinformatics 12(6): 1464-1469 (2015) doi:10.1109/TCBB.2015.2401020
  • S.J. Merrill and Y. Mu, Thyroid autoimmunity as a window to autoimmunity: An explanation for sex differences in the prevalence of thyroid autoimmunity, J. theor. Biol. 375: 95-100 (2015) doi:10.1016/j.jtbi.2014.12.015
  • P. Pradeep, R.J. Povinelli, S.J. Merrill, S. Bozdag, and D. Sem, Novel uses of in vitro data to develop quantitative biological activity relationship models for in vivo carcinogenicity prediction, Molecular Informatics 34 (4): 236-245 (2015) doi: 10.1002/minf.201400168
  • S.S. Kiware, G. Corliss, S. Merrill, D.W. Lwetoijera, G. Devine, S. Majambere, G.F. Killeen, Predicting scenarios for successful autodissemination of pyriproxyfen by malaria vectors from their resting sites to aquatic habitats; Description and simulation analysis of a field-parametrized model, PLoS One 10(7): e0131825 (2015) doi:10.1371/journal.pone.0131835
  • S.J. Merrill, Why study statistics? Chapter 3 in Statistics for the Curious: Why Study Statistics, K. Vaidya, ed., Curious Academic Publishing, 2015.
  • S.J. Merrill, M. Subramanian, D.E. Godar, Worldwide cutaneous malignant melanoma incidences analyzed by sex, age, and skin type over time (1955-2007): Is HPV infection of androgenic hair follicular melanocytes a risk factor for developing melanoma exclusively in people of European-ancestry? Dermato-Endocrinology 8(1): e1215391 (2016) doi:10.1080/19381980.2016.1215391
  • P. Pradeep, R.J. Povinelli, S. White, S.J. Merrill, An Ensemble Model of QSAR Tools for Regulatory Risk Assessment, Journal of Cheminformatics 8:48 (2016) doi:10.1186/s13321-016-0164-0
  • B. Pandiyan, S.J. Merrill, and S. Benvenga, A homoclinic orbit in a patient-specific model of Hashimoto's Thyroiditis, Differential Equations and Dynamical Systems (2016). doi:10.1007/s12591-016-0335-5
  • D.E. Godar, M. Subramanian, S.J. Merrill, Cutaneous malignant melanoma incidences analyzed worldwide by sex, age, and skin type over personal Ultraviolet-B dose shows no role for sunburn but implies one for vitamin D3, Dermato-Endocrinology 9(1): e1267077 (2017) doi:10.1080/19381980.2016.1267077
  • D.E. Godar, M. Subramanian, S.J. Merrill, Cutaneous malignant melanoma incidences analyzed worldwide by sex and skin type over advancing age of males and females: Evidence estrogen and androgenic hair are risk factors, Journal of Epidemiological Research 3(1): 42-50 (2017) doi:10.5430/jer.v3n1p42
  • L.C. Savery, R. Vinas, A. Nagy, P. Pradeep, S.J. Merrill, A.M. Hood, S.G. Malghan, P.L. Goering, R.P. Brown, Deriving a provisional tolerable intake for intravenous exposure to silver nanoparticles released from medical devices, Regulatory Toxicology and Pharmacology 85: 108-118 (2017) doi:10.1016/j.yrtph.2017.01.007
  • J. Sharma, B. Wisniewski, E. Paulson, J. Obaoye, S.J. Merrill, and A.L. Manogaran, De novo [PSI+] prion formation involves multiple pathways to form infectious oligomers, Scientific Reports 7:76 (2017) doi:10.1038/s41598-017-00135-6
  • Y. Mu, D.E. Godar, S.J. Merrill, A perspective on the challenges and issues in developing biomarkers for human allergic risk assessments, Biomarkers in Medicine 11(7):523-526 (2017) doi:10.2217/bmm-2017-0137
  • D.E. Godar, R. Gurov, S.J. Merrill, All sites but skin cancer incidences analyzed worldwide by sex, age, and skin type over time (1955-2007), advancing age, and UVB dose reveals important carcinogenic drivers, Journal of Epidemiological Research 3(2):65-80 (2017) doi:10.5430/jer.v3n2p65
  • B. T. Wisniewski, J. Sharma, E. R. Legan, E. Paulson, S. J. Merrill, and A. L. Manogaran, Toxicity and Infectivity: insights from de novo prion formation, Current Genetics, (2017) doi:10.1007/s00294-017-0736-1
  • D.E. Godar and S.J. Merrill, Untangling the most probable role for vitamin D3 in autism, Dermato-Endocrinology 9(1): e1387702 (2017) doi:10.1080/19381980.2017.1387702
  • B. Pandiyan, S.J. Merrill, F. Di Bari, A. Antonelli, S. Benvenga, A patient-specific treatment model for Graves' hyperthyroidism, Theoretical Biology & Medical Modelling 15(1) (2018) doi:10.1186/s12976-017-0073-6
  • S.J. Merrill and S.B. Minucci, Thyroid autoimmunity: an interplay of factors, Vitamins and Hormones, 106:129-146 (2018) doi:10.1016/bs.vh.2017.07.001
  • S.J. Merrill and B. Pandiyan, Untangling thyroid autoimmunity through modeling and simulation, Frontiers in Bioscience (Landmark Ed) 23:1889-1901 (2018) doi:10.2741/4679
  • B. Pandiyan and S.J. Merrill, A model of the cost of delaying treatment of Hashimoto's thyroiditis: thyroid cancer initiation and growth, Mathematical Biosciences and Engineering 16(6) 8069-8091 (2019) doi:10.3934/mbe.2019406.
  • K. Irabor and S.J. Merrill, Bifurcation in Markov chains with ecological examples, Nonlinear Dynamics, Psychology and Life Sciences, to appear (2019).


Doctoral Students

1988 Xuncheng Huang  Mathematical analysis of population models 

1992 Ondine Harris  The Polymerase Chain Reaction: A Stochastic Model, Methods of Quantification, and Applications to HIV

1993 Zhixiong He Mathematical models of muscle response to periodic stimuli 

1996 Xing Wu  Dynamical systems in the modeling of lampry fictive swimming 

2001 Brian Murphy Modeling the time to engraftment of white blood cells and platelets following autologous peripheral blood stem cell transplantation 

2008 Shivani Ratnakumar Markov chain modeling of ECG gated live left atrial fluoroscopy variability to establish a well-defined basis for rigid registration to a 3D CT image

2011 Balamurugan Pandiyan Mathematical modeling and dynamical analysis of the operation of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis

2015 Prachi Pradeep Hybrid computational toxicology models for regulatory risk assessment

2015 Mohammad Adibuzzaman Computational approached for monitoring of health parameters and their evaluation for application in clinical setting (with Sheikh Iqbal Ahamed)

2019 Kehinde Irabor Bifurcation in weighted digraphs and application in ecology

2019 Xuyong Yu Evaluating electrode-tissue contact force using cardiac image processing technology


Special Interest




Stephen J. Merrill
Department MSSC Cudahy Hall
Marquette University
P.O. Box 1881
Milwaukee, WI 53201-1881

Phone: (414)-288-7573 (Department Office)
Fax: (414)-288-5472