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Department of MathematicsWinnipeg, Manitoba, Canada, R3T 2N2
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A. B. Gumel
Graduate Students:C. Podder, S. Sharomi, A. Niger, D. MelesseResearch Areas:Mathematical Biology, Dynamical Systems, Computational Mathematics Personal WebsiteResearch Interests:Mathematical Biology: This entails designing robust mathematical models (deterministic or stochastic) for monitoring the spread of some emerging and re-emerging human diseases of public health importance in a given population (epidemiology). This also involves modelling the host-pathogen dynamics (pathogenesis) in the body of an infected individual. The main goal is to devise, via mathematical modelling, effective mechanisms for controlling or eliminating disease spread in a community and/or in vivo. Some of the diseases of interest include: childhood diseases, dengue, HIV/AIDS, influenza (including pandemic influenza), malaria, mycobacterium tuberculosis, SARS, West Nile virus etc. Applied Dynamical Systems: This involves using
dynamical systems theories and methodologies (e.g. stability,
bifurcation and perturbation theories) to gain insights into the
qualitative behaviour of non-linear dynamical systems associated with
the mathematical modelling of real-life phenomena arising in the
natural and engineering sciences (such as chemical kinetics, non-linear
oscillations, pharmacokinetics, industrial mathematics, finance,
thermo-elasticity, epidemiology and pathogenesis of human diseases
etc.) . In the context of disease modelling, for instance, we are
typically interested in issues such as: (i) existence of equilibria,
(ii) existence or non-existence of periodic solutions, (iii) stability
of solutions (local and global), types of bifurcations etc…and how all
these features can be used to formulate an effective public health
strategy to combat the spread of a certain disease. Computational Mathematics: My interest in this is
based on two main components. The first, based on the theory of
nonstandard finite-difference discretization, is focussed on the design
of competitive numerical techniques for finding quantitative solutions
of models arising from modelling real-life phenomena in the natural and
engineering sciences. The emphasis is that the numerical method is free
of scheme-dependent instabilities (such as contrived oscillations,
bifurcations and chaos) and convergence to spurious (false) solutions.
In other words, the method must provide computed solutions that are
qualitative consistent with those of the governing continuous model
being approximated. The second component is about the design of efficient parallel
algorithms, via the use of the Method of Lines semi-discretization, for
solving some computationally-intensive
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