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Stephen J. Merrill - Professor 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


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 – registration and 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

Journal of Immunological Methods (vol. 374 issues 1-2) in November 2011 :


                                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.

The issue also reported the results of the machine learning competition on prediction of HLA class I binding peptides.

Most Recent Publications (Earlier Publications)

·         S.J. Merrill and B.M. Murphy, Detecting autocatalytic dynamics in data modeled by a compartmental model, Math. Biosci. 180 (2002), 255-262.

  • 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. Viñas, 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



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)


Current Doctoral Students


    Emily Paulson Dynamics of prion-like accumulation and pattern formation in yeast

    Xuyong Yu Cardiac electrophysiology – catheter tracking and analysis

    Kehinde Irabor The mathematics of evaluating ecological corridors



Special Interest




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

Phone: (414)-288-5237
Fax: (414)-288-5472