Modelling the aqueous transport of an infectious pathogen in regional communities: application to the cholera outbreak in Haiti.

A mathematical model is developed to describe the dynamics of the spread of a waterborne disease among communities located along a flowing waterway. The model is formulated as a system of reaction-diffusion-advection partial differential equations in this spatial setting. The compartments of the model consist of susceptible, infected, and recovered individuals in the communities along the waterway, together with a term representing the pathogen load in each community and a term representing the spatial concentration of pathogens flowing along the waterway. The model is applied to the cholera outbreak in Haiti in 2010.

Spatial models of vector-host epidemics with directed movement of vectors over long distances.

We investigate a time-dependent spatial vector-host epidemic model with non-coincident domains for the vector and host populations. The host population resides in small non-overlapping sub-regions, while the vector population resides throughout a much larger region. The dynamics of the populations are modeled by a reaction-diffusion-advection compartmental system of partial differential equations. The disease is transmitted through vector and host populations in criss-cross fashion. We establish global well-posedness and uniform a prior bounds as well as the long-term behavior. The model is applied to simulate the outbreak of bluetongue disease in sheep transmitted by midges infected with bluetongue virus. We show that the long-range directed movement of the midge population, due to wind-aided movement, enhances the transmission of the disease to sheep in distant sites.

The work of Glenn F. Webb.

It is my distinct pleasure to introduce this volume honoring the 70th birthday of Professor Glenn F. Webb. The existence of this compiled volume is in itself a testimony of Glenn's dedication to, his pursuit of, and his achievement of scientific excellence. As we honor Glenn, we honor what is excellent in our profession. Aristotle clearly articulated his concept of excellence. ``We are what we repeatedly do. Excellence, then, is not an act, but a habit." As we look over the course of his career we observe ample evidence of Glenn Webb's habitual practice of excellence. Beginning with Glenn's first paper [1], one observes a constant stream of productivity and high impact work. Glenn has authored or co-authored over 160 papers, written one research monograph, and co-edited six volumes. He has delivered plenary lectures, colloquia, and seminars across the globe, and he serves on the editorial boards of 11 archival journals. He is a Fellow of the American Mathematical Society. Glenn's scientific career chronicles an evolution of scientific work that began with his interest in nonlinear semigroup theory and leads up to his current activity in biomedical mathematics. At each stage we see seminal contributions in the areas of nonlinear semigroups, functional differential equations, infinite dimensional dynamical systems, mathematical population dynamics, mathematical biology and biomedical mathematics. Glenn's work is distinguished by a clarity and accessibility of exposition, a precise identification and description of the problem or model under consideration, and thorough referencing. He uses elementary methods whenever possible but couples this with an ability to employ power abstract methods when necessitated by the problem.