Article ID Journal Published Year Pages File Type
467992 Computers & Mathematics with Applications 2015 26 Pages PDF
Abstract

In this paper, we are concerned with a model of the indirect transmission of an epidemic disease between two spatially distributed host populations having non-coincident spatial domains with nonlocal and cross-diffusion, the epidemic disease transmission occurring through a contaminated environment. The mobility of each class is assumed to be influenced by the gradient of the other classes. We address the questions of existence of weak solutions and existence and uniqueness of classical solution by using, respectively, a regularization method and an interpolation result between Banach spaces. Moreover, we propose a finite volume scheme and proved the well-posedness, nonnegativity and convergence of the discrete solution. The convergence proof is based on deriving a series of a priori estimates and by using a general LpLp compactness criterion. Finally, the numerical scheme is illustrated by some examples.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science (General)
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