Dr. Mubayi is a computational and mathematical researcher, and his research program focuses on ecological modeling and dynamics of neglected tropical diseases in human populations. His research is driven by complexity inherent at the vector-host interface in tropical countries, where multi-host pathogens such as Leishmania or Trypanosoma Cruzi persist and adapt to novel environments. Dr. Mubayi combines theoretical models to field data in order to deepen understanding of fundamental principles of disease transmission and adaptation and apply those principles to interpret observed patterns, uncover driving mechanisms, and design effective control policies. His research often involves the development of new mathematical tools, in nonlinear dynamics and stochastic process, for ameliorating the impact of neglected tropical diseases for impoverished populations.
Dr. Rapti’s specializes in the use of differential equations in mathematical biology. She has studied the relations between the thermal denaturation profiles of DNA sequences and the location of promoters-regions of DNA providing a control point for regulated gene transcription-and other significant regulatory regions. Dr. Rapti is also working on models that describe DNA configurations and dynamics, disease models for Daphnia (waterflea), and how community ecology—such as competitors and predators—shape the epidemics.