Professor & The Michael and Eugenia Brin Endowed E-Nnovate Chair in Mathematics
I am a Professor of Mathematics (and The Michael and Eugenia Brin Endowed E-Nnovate Chair in Mathematics) at the Department of Mathematics, University of Maryland, College Park. My research work focuses on using mathematical approaches (modeling, rigorous analysis, and data analytics) to gain insight and provide understanding on the transmission dynamics of emerging and re-emerging infectious diseases of public health significance. Specifically, I design, analyze, parameterize, and simulate novel models for the transmission dynamics and control of emerging and re-emerging infectious diseases. My research also involves the qualitative theory of nonlinear dynamical systems arising in the mathematical modeling of phenomena in population biology (ecology, epidemiology, immunology etc.) and computational mathematics (with emphasis on the design of robust numerical methods that give results that are dynamically-consistent with the governing continuous-time model being discretized). The ultimate objective of my research work, in addition to the development of advanced (and perhaps novel) mathematical theory and methodologies for studying nonlinear dynamical systems arising in population biology, is to contribute to the development of effective public health policy for controlling and mitigating the burden of emerging and re-emerging infectious diseases.
I am a mathematical biologist, who specialize in designing, rigorously analyzing and parameterizing novel mathematical models for gaining insight and understanding on the transmission dynamics and control of emerging and re-emerging infectious diseases of public health significance. My team and I have addressed research questions pertaining to the mathematics of the ecology, epidemiology and immunology of some infectious diseases of humans and other animals. We are currently focused on the following research questions and/or projects:
The mathematical models we design are often of the form of deterministic systems of nonlinear differential equations (ordinary, partial or functional). We use or develop dynamical systems theories and methodologies for studying the qualitative dynamics of these models, aimed at determining, in parameter space, conditions for the persistence or effective control of the diseases being modeled. Specifically, we are interested in proving theorems for the existence and asymptotic stability of the steady-state solutions of the models, and in characterizing the associated bifurcation types. Statistics play a major role in our research work. We specifically use optimization and inverse problem approaches to fit models to data, estimate unknown parameters (needed for model validation and cross-validation), make predictions and carry out global uncertainty and sensitivity analysis for the parameters of the models. Our work also involves some computational component. The nonlinearity and large dimensionality of the models we often deal with necessitate the use of robust numerical discretization approaches to find approximations of their solutions. We are specifically interested in designing numerical methods that are dynamical-consistent (i.e., preserve the essential physical properties) of the governing continuous-time models being discretized.