ARTICLE
SPATIO-TEMPORAL MATHEMATICAL MODELING OF INFECTIOUS DISEASES WITH CROSS DIFFUSION EFFECTS
- JP Journal of Mathematical Sciences , Volume (35) : 1-35
Discipline :
Mathématiques
Auteur(s) :
SAFIMBA SOMA , SIAKA KAMBELE and ABOUDRAMANE GUIRO
Auteur(s) tagués :
SOMA Safimba
Renseignée par : SOMA Safimba
Résumé
In this paper, we study analytically a class of nonlinear parabolic reaction- diffusion systems modeling the spread of infectious diseases with cross- diffusion terms. This model is governed by an S-I-R type system. First, we
prove the global existence of weak solution to this class of system by means of an approximation process, the Faedo-Galerkin method, some a priori estimates and compactness arguments. Then, using Gronwall’s lemma, we establish an existence and uniqueness result of weak solution for this class of systems without the cross-diffusion terms.
Mots-clés
Keywords and phrases: infectious diseases, S-I-R model, cross-diffusion system, weak solutions, Faedo-Galerkin.