A generalization of the Archimedean double sequence

A reaction-diffusion system involving an integrodifferential linear parabolic equation and a nonlinear ordinary differential equation is studied, under third type boundary conditions. Such a system may be used to describe the evolution of a class of man-environment epidemics. Conditions are given for the existence and the asymptotic stability of a unique nontrivial equilibrium solution, by using monotone iteration techniques.