Research Interests: 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:
- What is the impact of anthropogenic climate and environmental changes on the global burden and distribution of vector-borne diseases, such as malaria, dengue fever, Zika and West Nile virus?
- Is there a connection between insecticide resistance and malaria epidemiology? This entails designing a novel genomic-epidemiology framework for malaria transmission dynamics in a population, where the malaria vector (Anopheles mosquitoes) are stratified according to genotype.
- What is the impact of land use changes and human mobility on the global burden and distribution of infectious diseases?
- Mathematics of the One Health Initiative … where public health is viewed holistically within the human-animal-environment nexus. This is critical in using mathematical approaches to predict the likelihood, and effective control and mitigation, of major disease outbreaks and pandemics.
- Assessment of nonpharmaceutical and pharmaceutical control and mitigation strategies against human and other animal diseases of major public health significance.
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.