A degenerate nonlinear diffusion system with boundary feedbackδ

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Abstract
A class of man-environment epidemic systems with integral boundary (feedback is presented. Existence, uniqueness and comparison theorems are given for a system involving a nonlinear degenerate parabolic equation and a semilinear parabolic equation under a nonlinear boundary condition which couples the two equations. This system includes the epidemic model. Conditions for the existence and the asymptotic stability of a unique nontrivial equilibrium solution are stated for this model.