The 2013 AARMS Summer School

Theme: Dynamical Systems and Mathematical Biology
Time and location: July 15-Aug. 9, 2013, Memorial University of Newfoundland
School Director: Dr. Xiaoqiang Zhao, MUN

The summer school is intended for graduate students and promising undergraduate students from all parts of the world. Each participant is expected to register for at least two of the four courses. Each course consists of five ninety-minute lecture sessions each week. These are graduate courses approved by MUN and we will facilitate transfer credit to the extent possible.

The class schedule can be found here.


  • Stochastic Modeling with Applications in BiologyInstructors: Drs. Linda Allen and Edward Allen, Texas Tech University, USAPrerequisites: Basic undergraduate courses in ordinary differential equations, probability theory, and linear algebra with some understanding of MATLAB programming.
  • Reaction-Diffusion Equations and ApplicationsInstructor: Dr. Stephen Cantrell, University of Miami, USAPrerequisites: The lectures are chiefly based on the book “Spatial ecology via Reaction-Diffusion Equations” by Stephen Cantrell and Chris Cosner. At a minimum students should be familiar with partial differential equations at a level equivalent to a senior undergraduate or master’s level graduate course in the subject. Some familiarity with basic facts from dynamical systems and a general level of mathematical sophistication comparable to that one would expect from a first year graduate course in real analysis is desirable.
  • Mathematical Methods to Gain Biological InsightsInstructor: Dr. Odo Diekmann, Utrecht University, The NetherlandsPrerequisites: Basic knowledge about linear algebra, analysis, ordinary differential equations, stochastic processes. The key point, however, is the attitude: students should be willing to quickly fill in gaps in background knowledge.This is a master course for math students about mathematical methods to gain insight in the mechanisms underlying biological phenomena. In the course, a lot of attention is paid to “translation”: how do we get from biological information to a mathematical formulation of questions? And what do the mathematical results tell us about biological phenomena? In addition, the course aims to introduce general physical ideas about time scales and spatial scales and how these can be used to great advantage when performing a mathematical analysis. “Lecture Notes in progress” can be downloaded at
  • Mathematical Modelling in Developmental Biology and MedicineInstructor: Dr. Philip Maini, University of Oxford, UKPrerequisites: Basic theory of ordinary and partial differential equations: solution of simple ODEs and PDEs; Linear matrix algebra: eigenvectors and eigenvalues; and Some modelling experience would help but is not essential.

Instructor Bios

Edward Allen is a professor of mathematics at Texas Tech University. He graduated with a Ph.D. degree in mathematics from the University of Tennessee in 1983. Before receiving his doctoral degree in mathematics, he obtained B.S. and M.S. degrees in nuclear engineering from the University of Wisconsin and worked as a professional nuclear engineer at Oak Ridge National Laboratory.

Edward Allen performs research in model formulation, analysis, and computation of deterministic and stochastic models in biology, nuclear engineering, and physics with over 70 papers in technical journals. He has directed twenty-six MS theses and six PhD dissertations. He is the author or co-author of two graduate texts “Modeling with Ito Stochastic Differential Equations” and “Classical and Modern Numerical Analysis”. In addition to regularly teaching graduate courses in stochastic differential equations (SDEs) and numerical analysis at Texas Tech University, he has given workshops in the derivation and computation of stochastic differential equation models at the National Center for Theoretical Sciences at the National Tsing Hua University in Taiwan, the MAA Professional Enhancement Program at Texas Tech University, the Mathematical Biosciences Institute at Ohio State University, and the National Institute for Mathematical and Biological Systems at the University of Tennessee. He is scheduled in the summer of 2013 to present an intensive course in SDEs for the Atlantic Association for Research in Mathematical Sciences at the Memorial University of Newfoundland.

Linda J. S. Allen is a professor of mathematics at Texas Tech University. She received her M.S. and Ph.D. degrees in mathematics from the University of Tennessee. Her research interests include mathematical modeling of biological systems, applying discrete and continuous dynamical systems and stochastic processes to problems in epidemiology, population biology, immunology, and plant pathology. She is the author of two textbooks, An Introduction to Mathematical Biology and An Introduction to Stochastic Processes, and over 80 papers in mathematical biology. She has directed or co-directed 39 M.S. and PhD theses and 9 undergraduate research projects. Professionally, she serves on the editorial board for Mathematical Biosciences, Journal of Theoretical Biology, Journal of Difference Equations and Applications and Journal of Biological Dynamics. Over the past 8 years, Linda Allen has given invited lectures on deterministic and stochastic models in epidemiology and population biology at workshops and short courses held at Banff Research Station, York University, and University of Alberta in Canada, National Tsing Hua University in Taiwan, Universidade de Porto in Portugal, and Mathematical Biosciences Institute, Ohio State University and National Institute for Mathematical and Biological Synthesis, University of Tennessee, in the United States.

Stephen Cantrell received his B.S. in mathematics summa cum laude from Furman University in 1976 and his Ph.D. in mathematics from the University of Utah in 1981, under the supervision of Klaus Schmitt. After one year at Southwest Texas State University in San Marco, Texas, he joined the faculty of the Department of Mathematics at the University of Miami in the fall of 1982 as an Assistant Professor, rising to the rank of Associate Professor in 1987 and to the rank of Professor in 1992. Since 2007 he has served as Director of the University of Miami Institute of Theoretical and Mathematical Ecology. He currently is an Associate Editor of Mathematical Biosciences and Engineering. Cantrell’s areas of mathematical specialization are nonlinear analysis, partial differential equations, and mathematical ecology and epidemiology. Cantrell’s 30 year plus collaboration on these topics with his Miami colleague Chris Cosner has led to over 60 joint papers, the book Spatial Ecology via Reaction-Diffusion Equations (John Wiley and Sons 2003) and the recent volume of essays Spatial Ecology (co-edited with Shigui Ruan also of the University of Miami) (CRC/Chapman Hall 2009). Much of this work has also been in conjunction with the research groups of Yuan Lou at Ohio State University, William Fagan at the University of Maryland and John Beier of the Miller School of Medicine at the University of Miami. Cantrell’s current research interests include the ecological effects and evolution of dispersal, the ecological foundations of the establishment of vector-borne disease in arid environments, and the interplay of phenology, asynchronous demography and dispersal and evolutionary adaptation in the face of climatic change.

Odo Diekmann worked at the CWI in Amsterdam from 1974 to 1995, obtaining his PhD degree at the University of Amsterdam in 1978. From 1986 to 1995 he was part time professor in Mathematical Biology at the University of Leiden, where he collaborated closely with Hans Metz. In 1995 he became professor of Applied Mathematics at Utrecht University. His fields of interest are Population Dynamics (including Infectious Disease Epidemiology and Evolution) and Dynamical Systems (notably delay equations). He is a Honorary Editor of the Journal of Mathematical Biology and has written, jointly with others, various books. The most recent of these MATHEMATICAL TOOLS FOR UNDERSTANDING INFECTIOUS DISEASE DYNAMICS (together with Hans Heesterbeek and Tom Britton) just appeared at Princeton University Press.

Philip K. Maini received his B.A. in mathematics from Balliol College, Oxford, in 1982 and his DPhil in 1985 under the supervision of Prof J.D. Murray, FRS. After completing his studies he spent a year as an Assistant Master at Eton College before returning to the CMB in 1987 as a Junior Research Fellow at Wolfson College, Oxford. In 1988 he was appointed Assistant Professor in the Mathematics Department at the University of Utah, Salt Lake City before returning to Oxford two years later, initially as a University Lecturer and then as Professor and Director of the CMB. He is currently on the editorial boards of a large number of journals, including serving as the Editor-in-Chief of the Bulletin of Mathematical Biology. He has also been an elected member of the Boards of the Society for Mathematical Biology (SMB) and European Society for Mathematical and Theoretical Biology (ESMBTB). He is a Fellow of the IMA, a SIAM Fellow, and was elected Miembro Correspondiente, La Academia Mexicana de Ciencias (AMC) in 2011.

His present research projects include the modelling of avascular and vascular tumours, normal and abnormal wound healing, and a number of applications of mathematical modelling in pattern formation in early development, as well as the theoretical analysis of the mathematical models that arise in all these applications. He has over 300 publications in the field and has held visiting positions at a number of universities worldwide. He was a Distinguished Foreign Visiting Fellow, Hokkaido University (2002). In 2005 he was elected Honorary Guest Professor, University of Electronic Science Science and Technology of China, Chengdu, in 2006 appointed to a 3-year Adjunct Professorship at the School of Mathematical Sciences, Queensland University of Technology, Brisbane (and again in 2012), in 2010 appointed to a 3-year Adjunct Professorship at Lincoln University, Christchurch, New Zealand, and also appointed as a Distinguished Research Fellow at the African Institute for Mathematical Sciences (AIMS), South Africa.

He co-authored a Bellman Prize winning paper (1997), was awarded a Royal Society Leverhulme Trust Senior Research Fellowship for 2001-2 and a Royal Society-Wolfson Research Merit Award (2006-11). In 2009 he was awarded the LMS Naylor Prize and Lectureship.

Associated Workshop

In the middle of the summer school, there is an AARMS Workshop on Mathematical Biology, which will be held in the campus of Memorial University, St. John’s, July 27-29, 2013. Please let the Summer School Director know if you wish to also attend the workshop.

To Apply

The deadline for applications is 15 March 2013. To submit an application, please download and complete this textfile and return it by e-mail to Dr. Xiaoqiang Zhao at the address listed below.

Also, be sure to ask your supervisor or department head to send a reference letter which (a) clearly mentions your name and (b) comments on your preparation for the two courses you have selected.

The AARMS Summer School will pay the accommodation expenses of the school’s participants, but is unable to reimburse any costs of travel.

Travel Support

Note that the 2013 AARMS summer school is one of events in the pan-Canadian thematic year “Models and Methods in Ecology, Epidemiology and Public Health”. Thus, the school participants at US institutions can apply for travel support from a grant from the US National Science Foundation. To apply, please send a brief CV (2 pages maximum) and a statement of interest including estimated cost for travel and accommodation (1 page maximum) in a single file (pdf format) to Frithjof Lutscher ( Please also arrange for one letter of support to be sent to the same address. All emails should have the subject line “NSF support for M2E2-name of event”. Review of applications begins two months prior to the event and continues as long as funds are available.

Accommodation in University Residence

The summer school has booked 35 single rooms with the University Residence office, which was given a list of our selected students who are willing to live in the University Residence. The summer school will pay this expense of accommodation directly to the University Residence. However, these students should confirm their check-in and check-out dates directly to the University Residence office in a timely fashion. You can make phone calls to this office at 709-864-7933, or send your e-mail to Conferences Someone should get back to you within two days if you email. You may also ask this office where you should go upon arrival (that is, the address of your living place).

Contact Information

For further information contact

  • Dr. Xiaoqiang Zhao
  • Department of Mathematics and Statistics
  • Memorial University of Newfoundland
  • St. John’s, Newfoundland & Labrador
  • Canada A1C 5S7
  • Phone: (709) 864-8098

Other Information


For a list of participants at the 2013 Summer School please click here.


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