Mathematical Analysis and Pattern Formation for a Partial Immune System Modeling the Spread of an Epidemic Disease
Source: Acta Applicandae Mathematicae, Volume 115, Number 1, July 2011 , pp. 17-42(26)
Abstract:Our motivation is a mathematical model describing the spatial propagation of an epidemic disease through a population. In this model, the pathogen diversity is structured into two clusters and then the population is divided into eight classes which permits to distinguish between the infected/uninfected population with respect to clusters. In this paper, we prove the weak and the global existence results of the solutions for the considered reaction-diffusion system with Neumann boundary. Next, mathematical Turing formulation and numerical simulations are introduced to show the pattern formation for such systems.
Document Type: Research Article
Affiliations: 1: Institut de Mathématiques de Bordeaux UMR CNRS 525, Université Victor Segalen Bordeaux 2, 33076, Bordeaux Cedex, France, Email: firstname.lastname@example.org 2: Ecole Centrale de Nantes, Département Informatique et Mathématiques, Laboratoire de Mathématiques Jean-Leray (UMR 6629 CNRS) 1, rue de la Noé, 44321, Nantes, Cedex 3, France, Email: Mazen.Saad@ec-nantes.fr
Publication date: July 1, 2011