Applied Mathematics, Mathematical Biology, Population Dynamics and Evolution, Perturbation Techniques, Differential Equations, Dynamical Systems, Modeling Complex Biological Systems, Markov Decision Processes.
I use Mathematics and Computational methods to understand the transmission dynamics of emerging and re-emerging infectious diseases, with the end goal being disease control. I take the one health approach in which the end goal of control can be understood from a multi-faceted complex view points, where interactions between players contribute in different ways towards a successful transmission of disease within a society. For example, in malaria transmission, where there are three interacting populations, the human, the pathogen that causes malaria and the mosquitoes responsible for transmitting the pathogen from one human to another, there are three living interacting populations each with an evolutionary need to survive. I use differential equations (ODE and PDEs) to elucidate the complexities that exists due to these interactions and model how these interactions enhances disease transmission. While I have focused on the malaria disease, the work I do can be extended to other mosquito-borne diseases such as Dengue, Zika, Chikungunya and lymphatic filariasis. Additionally, in an effort to control these diseases, decisions have to be made and the stake holders and decision makers can enable or enhance the kind of responses and control achieved. Thus I am interested in incorporating Markov Decision Processes (MDPs) and its variations via stochastic complex models in understanding the effects of such decisions on disease control.
I am also interested in the development of models applicable to transport phenomena from capillaries to tissues. Extensions to this research area exits, including unsteady flow for dosage therapy, and drug administration to tumor growth in cancer chemotherapy, and I am interested in these applications. The mathematics involve solving partial differential equations and also using asymptotic and perturbation techniques in analyzing partial differential equations. I also have interest in the mathematics that deals with chronic skin inflammation, a process by which dendritic cells (DCs) are constantly sampling antigen in the skin and migrating to lymph nodes where they induce the activation and proliferation of T cells. The T cells then travel back to the skin where they release cytokines that induce and maintain the inflammatory condition. This process is cyclic and ongoing. In the case of chronic inflammation, the desire is to interrupt this DC migration.