A high resolution finite difference method for a model of structured susceptible‐infected populations coupled with the environment |
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Authors: | Azmy S. Ackleh Baoling Ma Tingting Tang |
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Affiliation: | 1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana;2. Department of Mathematics, Millersville University of Pennsylvania, Millersville, Pennsylvania |
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Abstract: | We develop a general model describing a structured susceptible‐infected (SI) population coupled with the environment. This model applies to problems arising in ecology, epidemiology, and cell biology. The model consists of a system of quasilinear hyperbolic partial differential equations coupled with a system of nonlinear ordinary differential equations that represents the environment. We develop a second‐order high resolution finite difference scheme to numerically solve the model. Convergence of this scheme to a weak solution with bounded total variation is proved. Numerical simulations are provided to demonstrate the high‐resolution property of the scheme and an application to a multi‐host wildlife disease model is explored.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1420–1458, 2017 |
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Keywords: | convergence second order finite difference approximation susceptible‐infected structured epidemic model |
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