On a mathematical model for body tissue inflammation

Abstract

In the present paper I will try to prove the mathematical validity of a model on the localized bacterial infection for tissue inflammation. This model was proposed by Lauffenburger and Kennedy, and it describes the inflammatory response to bacterial invasion of body tissue. I prove the mathematical validity of the model by means of a positivity theorem, an existence theorem and a uniqueness theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension.