RESUMEN

We derive from a structured population model a system of delay differential equations describing the interaction of five subpopulations, namely susceptible and infected adult and juvenile reservoirs and infected adult vectors, for a vector borne disease with particular reference to West Nile virus, and we also incorporate spatial movements by considering the analogue reactiondiffusion systems with nonlocal delayed terms. Specific conditions for the disease eradication and sharp conditions for the local stability of the disease-free equilibrium are obtained using comparison techniques coupled with the spectral theory of monotone linear semiflows. A formal calculation of the minimal wave speed for the traveling waves is given and compared with field observation data.

RESUMEN

Brailovsky and Sivashinsky have proposed a model for pressure-driven combustion in the form of a degenerate parabolic system for temperature, concentration, and pressure. It is shown that the existence and uniqueness problem for traveling front solutions can be completely solved by exploiting the existing invariants and by phase plane methods. The approach yields exact propagation speeds which are noticeably larger than the approximations obtained so far.