How can we predict the long-term status of an ecosystem comprising interacting and competing species, which continue to move around in search of limited food and resources? What factors might lead to the extinction of, or to an infectious disease outbreak in, a particular species? How can neural networks - systems that work like a human brain, learning to "think" and to solve difficult problems based on previous experiences - be used in data mining applications, such as collecting and filtering through massive amounts of correlated information to find patterns? These are some of the questions my research seeks to answer. My scientific work, largely using delay differential equations and other infinite dimensional dynamical systems, aims to develop the theory and techniques of non-linear analysis and dynamical systems to resolve issues arising from “real-world” applications in ecology, epidemiology, data processing, and neural dynamics.
My work has been supported by a number of Canadian and international funding agencies including the Canada Research Chair Program (CRC), the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Institutes of Health Research (CIHR), the Social Sciences and Humanities Research Council (SSHRC), the Mathematics for Information Technology and Complex Systems (MITACS), the Geomatics for Informed Decisions (GEOIDE) and International Development Research Center (IDRC). These supports enable me to sustain a large research team, to conduct a multidisciplinary research program in industrial and applied mathematics, and to interact and collaborate with university researchers and industrial and public health policy experts. I am directing the Laboratory for Industrial and Applied Mathematics (LIAM) and the MITACS Centre for Disease Modeling at York University (CDM).
I am the Canada Research Chair partner leader of an Infectious Disease Management and Modeling project under the International Research Chairs Initiative (IRCI), a new partnership between the International Development Research Centre and the Canada Research Chairs Program.