title: 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.
authors.affiliation: Dipartimento di Matematica, Universitá di Pisa, Italy.
authors.forename: P
authors.initials: P
authors.lastname: Cerrai
mesh_terms: D006801:Humans; D007249:Inflammation; D008433:Mathematics; D015233:Models, Statistical