Dr. Abba Gumel

Personal

Prefix: Dr.
First Name: Abba
Last Name: Gumel

Summary

Research Interests: Scientific Computing, Mathematical Biology, Dynamical Systems, Modelling, Numerical Analysis.

Biography

Abba Gumel is a Full Professor in the Department of Mathematics and the Director of the Institute of Industrial Mathematical Sciences (IIMS) of the University of Manitoba. He received his Ph.D. from Brunel University (London, England). His main research interests are in (i) Mathematical Biology, (ii) Applied Dynamical Systems and (iii) Computational Mathematics. The main objective of his research work is to use mathematical theories and methodologies to gain insights into the transmission and control dynamics of human diseases of public health interest. He has supervised a number of research students (NSERC-funded summer undergraduate and graduate students) and postdoctoral fellows. Professor Gumel has been the coordinator of the Mathematical Biology Team of the IIMS since its inception in 1999, and represents the University of Manitoba on the Board of Directors of the Fields Institute for Research in Mathematical Sciences, Toronto. Professor Gumel is an active member of the Canadian Applied and Industrial Mathematics Society (CAIMS). In addition to serving on its various committees earlier, Professor Gumel was elected Secretary of CAIMS from 2007-2009 (he was re-elected for a second term: 2009-2011). Professor Gumel serves on the Outreach Committee of the Society for Mathematical Biology (SMB). Owing to its interdisciplinary nature, Professor Gumels work enjoys fruitful collaborations with mathematical and medical scientists from around the world. Professor Gumel has received the following research awards and honours:

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 re-emerging infectious diseases, aimed at assessing and determining optimal control strategies for an epidemic.

(2) Non-linear Dynamical Systems: Designining and using Dynamical Systems theories and tools to investigate the asymptotic dynamical behaviour of some real-life systems which are formulated in the form of deterministic, non-linear, ordinary differential equation systems.

(3) Computational Mathematics: Gumel's earlier work on Computational Mathematics was based on the design of efficient L_0-stable methods, via the use of the method of lines semi-discretization approach, for solving multi-dimensional partial differential equations. Gumel's main contribution in this area includes the design of a new family of L_0-stable methods which enable the solution of second-order linear parabolic and hyperbolic partial differential equations with or without time-dependent 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 computationally-expensive 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 finite-difference methods (non-standard methods) invented by Mickens a few decades ago. This class of methods is highly robust in capturing the asymptotic dynamics of many classes of real-life 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.

Dr. Gumel has published 36 journal articles.

Journal Publications

  1. 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): 2223-2232.
  2. 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): 503-524.
  3. A.B. Gumel, S.M. Moghadas and R.E. Mickens. Effect of a preventive vaccine on the dynamics of HIV transmission. Communications in Non-linear Science and Numerical Simulations. 9(6)(2004): 649-659.
  4. A.B. Gumel, S.M. Moghadas, Y. Yuan and P. Yu. Bifurcation and stability analyses of a 13-D SEIC model using normal form reduction and numerical simulations. Dynamics of Continuous, Discrete and Impulsive Systems, Series B. 10(2003): 317-330.
  5. C. Zhen, A.B. Gumel and R.E. Mickens. Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation. Numerical Methods for Partial Differential Equations. 19(3)(2003): 363-379.
  6. S.M. Moghadas and A.B. Gumel. Dynamical and numerical analyses of a generalized food-chain model. Applied Mathematics and Computation. 142(1)(2003): 35-49.
  7. S.M. Moghadas and A.B. Gumel. A mathematical study of a model for childhood diseases with non-permanent immunity. Journal of Computational and Applied Mathematics. 157(2)(2003): 347-363.
  8. A.B. Gumel, R.E. Mickens and B.D. Corbett. A non-standard finite-difference scheme for a model of HIV transmission and control. Journal of Computational Methods in Sciences and Engineering. 3(1)(2003): 91-98.
  9. A.B. Gumel and S.M. Moghadas. A qualitative study of a vaccination model with non-linear incidence. Applied Mathematics and Computation. 143(2-3)(2003): 409-419.
  10. R.E. Mickens and A.B. Gumel. Construction and analysis of a nonstandard finite difference scheme for the Burgers-Fisher equation. Journal of Sound and Vibration 257 (4)(2002): 791-797.
  11. A.B. Gumel. A competitive numerical method for a chemotherapy model of two HIV subtypes. Applied Mathematics and Computation. 131(2-3)(2002): 327-335.
  12. A.B. Gumel. Removal of contrived chaos in finite-difference methods. International Journal of Computer Mathematics. 79(9)(2002): 1033-1041.
  13. R.E. Mickens and A.B. Gumel. Numerical study of a nonstandard finite-difference scheme for the van der Pol equation. Journal of Sound and Vibration. 250(5)(2002): 955-963.
  14. 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): 147-155.
  15. S.M. Moghadas and A.B. Gumel. Global stability of a two-stage epidemic model with generalized non-linear incidence. Mathematics and Computers in Simulation. 60(1-2)(2002): 107-118.
  16. A.B. Gumel. Numerical modelling of the transmission dynamics of drug-sensitive and drug-resistant HSV-2.      Communications  in Non-linear Science and Numerical Simulation 6(1)(2001): 23-27.
  17. P. Yu and A.B. Gumel. Bifurcation and stability analyses for a coupled Brusselator model. Journal of Sound and Vibration. 244 (5)(2001): 795-820.
  18. A.B. Gumel, P.N. Shivakumar and B.M. Sahai.  A mathematical model for the dynamics of HIV-1 during the typical course of infection. Non-linear Analysis: Theory, Methods and Applications. 47(3)(2001): 1773-1783.
  19. W.T. Ang and A.B. Gumel. A boundary integral method for the three-dimensional heat equation subject to specification of energy. Journal of Computational and Applied Mathematics. 135  (2)(2001): 303-311.
  20. A.B. Gumel, T.D. Loewen, P.N. Shivakumar, B.M. Sahai, P. Yu and M.L. Garba. Numerical modelling of the       perturbation of HIV-1 during combination anti-retroviral therapy. Computers in Biology and Medicine  31(5)(2001): 287-301.
  21. 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.1-3 (2000): 169-181.
  22. A.B. Gumel, W.F. Langford, E.H. Twizell and J. Wu.  Numerical solutions for a coupled non-linear oscillator.     Journal of Mathematical Chemistry  28(4)(2000): 325-340.  
  23. 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): 475--483.
  24. A.B. Gumel Q. Cao and E.H. Twizell. A second-order scheme for the Brusselator reaction-diffusion system.    Journal of Mathematical Chemistry  26(1999): 297--316.
  25. 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): 13--24.
  26. A.B. Gumel. Numerical solutions for the canonical escape equation.         South East Asian Bulletin of Mathematics. 22(1998): 373--380.
  27. A.B. Gumel, K. Kubota and E.H. Twizell. A sequential algorithm for the non-linear dual-sorption model of percutaneous        drug absorption. Mathematical Biosciences. 152(1998): 87--103.
  28. A.B. Gumel, E.H. Twizell and M.A. Arigu.  L_0-stable parallel methods for multi-dimensional heat equation. Parallel Algorithms and Applications 11(1997): 13-25.
  29. A.B. Gumel, E.H. Twizell, M.A. Arigu and F. Fakhr. Numerical methods for a non-linear system arising in chemical kinetics. Pertanika Journal of Science and Technology. 5(2)(1997): 191-200.
  30. A.B. Gumel, W.T. Ang and E.H. Twizell. Efficient parallel algorithm for the two-dimensional diffusion equation subject to the specification of mass. International Journal of Computer Mathematics. 64 (1+2)(1997): 153-163.
  31. E.H. Twizell, A.B. Gumel and M.A. Arigu. Second-order, L_0-stable methods for partial differential equations with  time-dependent boundary conditions. Advances in Computational Mathematics. 6(3-4)(1996): 333-352.
  32. M.A. Arigu, E.H. Twizell and A.B. Gumel. Sequential and parallel methods for solving first-order hyperbolic equations.   Communications in Numerical Methods in Engineering. 12(1996): 557-568.
  33. W.T. Ang and A.B. Gumel. Multiple interacting planar cracks in an inisotropic multi-layered medium under an antiplane  shear stress: A hypersingular integral approach. Engineering Analysis with Boundary Elements. 2021(1996) 18(Iss.4): 297-303.
  34. M.A. Arigu, E.H. Twizell and A.B. Gumel.  Parallel algorithms for second-order hyperbolic equations.        Parallel Algorithms and Applications, 5(1995):  119-128.
  35. A.B. Gumel, E.H. Twizell, K. Kubota and M.A. Arigu. Higher-order parallel methods for a model of percutaneous drug absorption. International Journal of Computer Mathematics. 56(1995): 123-133.
  36. M.A. Arigu, E.H. Twizell and A.B. Gumel.  Parallel algorithms for fourth-order parabolic equations.    Parallel Algorithms and Applications. 5(1995): 273-286.