Abba Gumel is a Professor of Mathematics at the School of Mathematical and Statistical Science, Arizona State University (he is also the C. Castillo-Chavez Professor of Mathematical Biology). He received his PhD in Mathematics from Brunel University, England, in 1994, and has been Professor of Mathematics at the University of Manitoba, Canada (1999-2014).
Dr. Gumel works in the fields of applied nonlinear dynamical systems (bifurcation theory), mathematical biology and computational mathematics. His work is primarily focused on the use of mathematical approaches to gain insight into the transmission dynamics and control of emerging and re-emerging diseases of public health importance. His recent work addresses the problem of the effect of changes in climatic variables, such as temperature and rainfall, on the ecology and epidemiology of vector-borne diseases. He has co-authored over 100 peer-reviewed research papers and three edited books.
Dr. Gumel is a Fellow of ASU-Santa Fe Institute for Biosocial Complex Systems, African Academy of Science (FAAS) and Nigerian Academy of Science (FAS). He received numerous research awards and honors, including the 2004 Rh Award for Excellence in Interdisciplinary Research and Scholarship (the highest research award given to junior faculty at the University of Manitoba) and four merit awards for research excellence at the University of Manitoba (2007, 2008, 2009, 2010). Dr. Gumel serves on the editorial board of numerous journals.
Professor Gumel is actively involved in numerous science and technology capacity building efforts in the continent of Africa, notably via the Africa Institute of Science and Technology project (a pan African projected, spearheaded by the Nelson Mandela Institution, aimed at building world-class centers of academic excellence in research and training in science and technology across Africa), the US-Africa Biomath Initiative and the African Mathematical Institutes Network.
My research work spans three main areas, as briefly described below.
Mathematical Biology: This entails designing, and rigorously analyzing, robust mathematical models for gaining insight into the transmission and control mechanisms of some emerging and re-emerging diseases of humans and other animals. The models, which typically take the form of systems of deterministic non-linear autonomous (or non-autonomous) differential equations, are used to design effective strategies (leading to the formulation of realistic public health policy) for controlling the spread of diseases in a given population. We have addressed research questions pertaining to the ecology, epidemiology and immunology of some diseases of public health importance, such as childhood diseases, chlamydia, Ebola, herpes simplex virus, hepatitis C virus, HIV/AIDS, influenza (seasonal and pandemic), malaria and tuberculosis (human and bovine). Our current research focus is on assessing the role of climatic variables on the biology, ecology and epidemiology of vector-borne diseases.
Non-linear Dynamical
Systems: This involves using dynamical
systems theories and methodologies to analyze the
qualitative behaviour of non-linear dynamical systems
(discrete-time and continuous-time) associated with
the mathematical modelling of real-life phenomena
arising in the natural and engineering sciences, with
emphasis on disease transmission dynamics and control.
We are particularly interested in studying the
asymptotic dynamics of the resulting systems,
particularly determining conditions for the existence
and asymptotic stability (local or global) of the
associated steady-state solutions (equilibria, fixed
points or periodic).
Computational
Mathematics: I am primarily interested in
the design of dynamically-consistent finite-difference
methods for solving non-linear dynamical systems
associated with the mathematical modelling of physical
phenomena arising in the natural and engineering
sciences. The objective is that the resulting
numerical methods are free of scheme-dependent
instabilities (such as contrived oscillations,
bifurcations and chaos) and convergence to spurious
solutions. I am also interested in designing effective
L0-stable finite-difference methods for solving PDEs
(on a parallel architecture).