Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays

In this article, the validity of the comparison principle (CP) for weakly coupled quasi-linear cooperative systems with delays is proven. This is a powerful tool for studying the qualitative properties of the solutions. The CP is crucial in the proofs of the existence and uniqueness of weak solutions to cooperative reaction–diffusion systems presented here. Other direct consequences of the CP are the stability of the solution, the attenuation of long time periods, etc. An example model is given by spatial SEIR models with delays. They are suitable for modeling disease spread in space and time and can be described using a weakly coupled cooperative reaction–diffusion system. In this paper, spatial SEIR models with delays are considered in a continuous space. The emphasis is on the qualitative properties of the solutions, which are important for providing a mathematical basis for the model.