Name: Abba Gumel
Birthplace: Jigawa State, Nigeria.
Ph.D. Computational
Mathematics, Brunel University, England. 1993.
area: parallel and sequential algorithms for parabolic partial
differential equations
: Full
Professor, Department of Mathematics, University of Manitoba,
Canada.
Research Interests: Scientific Computing, Mathematical
Biology, Dynamical Systems, Modelling, Numerical Analysis.
Email: gumelab@cc.umanitoba.ca


Gumel: Born in Nigeria, received his Ph.D. in Computational
Mathematics from Brunel University in England and is now a tenured
Associate Professror at the University of Manitoba in Canada.
He has been making significant contributions
in many areas of Applied Mathematics including:
(1) Mathematical Biology: designing and qualitatively analysing
mathematical models for emerging and reemerging infectious diseases,
aimed at assessing and determining optimal control strategies
for an epidemic.
(2) Nonlinear Dynamical Systems: Designining and using Dynamical
Systems theories and tools to investigate the asymptotic dynamical
behaviour of some reallife systems which are formulated in the
form of deterministic, nonlinear, ordinary differential equation
systems.
(3) Computational Mathematics: Gumel's earlier work on Computational
Mathematics was based on the design of efficient L_0stable methods,
via the use of the method of lines semidiscretization approach,
for solving multidimensional partial differential equations.
Gumel's main contribution in this area includes the design of
a new family of L_0stable methods which enable the solution of
secondorder linear parabolic and hyperbolic partial differential
equations with or without timedependent source terms to be computed
on a parallel architecture, with each processor solving a linear
algebraic system at every time step using real arithmetic (as
against the computationallyexpensive complex arithmetic which
is often required in the process).
In collaboration with Ronald
Mickens, Gumel has, over the last few years, being actively
involved in the construction and theoretical framework of a new
class of finitedifference methods (nonstandard methods) invented
by Mickens a few decades ago. This class of methods is highly
robust in capturing the asymptotic dynamics of many classes of
reallife problems. Gumel has edited a special volume of the Journal
of Difference Equations and Applications marking Mickens' 60th
Birthday.
In November of 2003, Dr. Gumel was awarded a Young
African in Mathematics medal by the AMU and the ICMS.
We should note that Professor Gumel's lecture at CAARMS9
was first rate.
Abba Gumel with coauthor Ron
Mickens at CAARMS9
Journal
Publications
 A.B. Gumel, S. Ruan, T. Day, J. Watmough, F. Brauer,
P. Driesche, D. Gabrielson, C. Bowman, M.E. Alexander, S. Ardal,
J. Wu and B.M. Sahai. Modelling strategies for controlling
SARS outbreaks. Proceedings of the Royal Society, Series
B. 271(2004): 22232232.
 M.E. Alexander, C. Bowman, A.B. Gumel, S.M. Moghadas,
B.M. Sahai and R. Summers. A vaccination model for transmission
dynamics of influenza. SIAM Journal on Applied Dynamical
Systems. 3(4)(2004): 503524.
 A.B. Gumel, S.M. Moghadas and R.E.
Mickens. Effect of a preventive vaccine on the dynamics
of HIV transmission. Communications in Nonlinear Science
and Numerical Simulations. 9(6)(2004): 649659.
 A.B. Gumel, S.M. Moghadas, Y. Yuan and P. Yu. Bifurcation
and stability analyses of a 13D SEIC model using normal form
reduction and numerical simulations. Dynamics of Continuous,
Discrete and Impulsive Systems, Series B. 10(2003):
317330.
 C. Zhen, A.B. Gumel and R.E. Mickens. Nonstandard
discretizations of the generalized Nagumo reactiondiffusion
equation. Numerical Methods for Partial Differential Equations.
19(3)(2003): 363379.
 S.M. Moghadas and A.B. Gumel. Dynamical and numerical
analyses of a generalized foodchain model. Applied Mathematics
and Computation. 142(1)(2003): 3549.
 S.M. Moghadas and A.B. Gumel. A mathematical study
of a model for childhood diseases with nonpermanent immunity.
Journal of Computational and Applied Mathematics. 157(2)(2003):
347363.
 A.B. Gumel, R.E.
Mickens and B.D. Corbett. A nonstandard finitedifference
scheme for a model of HIV transmission and control. Journal
of Computational Methods in Sciences and Engineering.
3(1)(2003): 9198.
 A.B. Gumel and S.M. Moghadas. A qualitative study
of a vaccination model with nonlinear incidence. Applied
Mathematics and Computation. 143(23)(2003): 409419.
 R.E. Mickens and
A.B. Gumel. Construction and analysis of a nonstandard
finite difference scheme for the BurgersFisher equation. Journal
of Sound and Vibration 257 (4)(2002): 791797.
 A.B. Gumel. A competitive numerical method for a chemotherapy
model of two HIV subtypes. Applied Mathematics and Computation.
131(23)(2002): 327335.
 A.B. Gumel. Removal of contrived chaos in finitedifference
methods. International Journal of Computer Mathematics.
79(9)(2002): 10331041.
 R.E. Mickens and
A.B. Gumel. Numerical study of a nonstandard finitedifference
scheme for the van der Pol equation. Journal of Sound and
Vibration. 250(5)(2002): 955963.
 A.B. Gumel, Xuewu Zhang, P.N. Shivakumar, M.L. Garba
and B.M. Sahai. A new mathematical model for assessing therapeutic
strategies of HIV infection. Journal of Theoretical Medicine.
4(2)(2002): 147155.
 S.M. Moghadas and A.B. Gumel. Global stability of
a twostage epidemic model with generalized nonlinear incidence.
Mathematics and Computers in Simulation. 60(12)(2002):
107118.
 A.B. Gumel. Numerical modelling of the transmission
dynamics of drugsensitive and drugresistant HSV2.
Communications in Nonlinear Science and Numerical
Simulation 6(1)(2001): 2327.
 P. Yu and A.B. Gumel. Bifurcation and stability analyses
for a coupled Brusselator model. Journal of Sound
and Vibration. 244 (5)(2001): 795820.
 A.B. Gumel, P.N. Shivakumar and B.M. Sahai.
A mathematical model for the dynamics of HIV1 during the typical
course of infection. Nonlinear Analysis: Theory, Methods
and Applications. 47(3)(2001): 17731783.
 W.T. Ang and A.B. Gumel. A boundary integral method
for the threedimensional heat equation subject to specification
of energy. Journal of Computational and Applied Mathematics.
135 (2)(2001): 303311.
 A.B. Gumel, T.D. Loewen, P.N. Shivakumar, B.M. Sahai,
P. Yu and M.L. Garba. Numerical modelling of the
perturbation of HIV1 during combination antiretroviral therapy.
Computers in Biology and Medicine 31(5)(2001):
287301.
 A.B. Gumel, E.H. Twizell and P. Yu. Numerical and
bifurcation analyses of a population model of HIV chemotherapy.
Mathematics and Computers in Simulation. 54, Iss.13
(2000): 169181.
 A.B. Gumel, W.F. Langford, E.H. Twizell and J. Wu.
Numerical solutions for a coupled nonlinear oscillator.
Journal of Mathematical Chemistry 28(4)(2000):
325340.
 A.B. Gumel. On the numerical solution of the diffusion
equation subject to the specification of mass. Journal
of Australian Mathematics Society Series B 40(4)(1999):
475483.
 A.B. Gumel Q. Cao and E.H. Twizell. A secondorder
scheme for the Brusselator reactiondiffusion system.
Journal of Mathematical Chemistry 26(1999):
297316.
 A.B. Gumel and E.H. Twizell. Numerical analysis of
defects caused by thermolysis in an infinite cylindrical ceramic
moulding. Pertanika Journal of Science and Technology.
17(1)(1999): 1324.
 A.B. Gumel. Numerical solutions for the canonical
escape equation. South
East Asian Bulletin of Mathematics. 22(1998): 373380.
 A.B. Gumel, K. Kubota and E.H. Twizell. A sequential
algorithm for the nonlinear dualsorption model of percutaneous
drug absorption. Mathematical
Biosciences. 152(1998): 87103.
 A.B. Gumel, E.H. Twizell and M.A. Arigu. L_0stable
parallel methods for multidimensional heat equation. Parallel
Algorithms and Applications 11(1997): 1325.
 A.B. Gumel, E.H. Twizell, M.A. Arigu and F. Fakhr.
Numerical methods for a nonlinear system arising in chemical
kinetics. Pertanika Journal of Science and Technology.
5(2)(1997): 191200.
 A.B. Gumel, W.T. Ang and E.H. Twizell. Efficient parallel
algorithm for the twodimensional diffusion equation subject
to the specification of mass. International Journal of
Computer Mathematics. 64 (1+2)(1997): 153163.
 E.H. Twizell, A.B. Gumel and M.A. Arigu. Secondorder,
L_0stable methods for partial differential equations with
timedependent boundary conditions. Advances in Computational
Mathematics. 6(34)(1996): 333352.
 M.A. Arigu, E.H. Twizell and A.B. Gumel. Sequential
and parallel methods for solving firstorder hyperbolic equations.
Communications in Numerical Methods in Engineering.
12(1996): 557568.
 W.T. Ang and A.B. Gumel. Multiple interacting planar
cracks in an inisotropic multilayered medium under an antiplane
shear stress: A hypersingular integral approach. Engineering
Analysis with Boundary Elements. 2021(1996) 18(Iss.4):
297303.
 M.A. Arigu, E.H. Twizell and A.B. Gumel. Parallel
algorithms for secondorder hyperbolic equations.
Parallel Algorithms and Applications, 5(1995):
119128.
 A.B. Gumel, E.H. Twizell, K. Kubota and M.A. Arigu.
Higherorder parallel methods for a model of percutaneous drug
absorption. International Journal of Computer Mathematics.
56(1995): 123133.
 M.A. Arigu, E.H. Twizell and A.B. Gumel. Parallel
algorithms for fourthorder parabolic equations.
Parallel Algorithms and Applications. 5(1995):
273286.
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