The dynamics of a one-dimensional fox-rabies model. (English) Zbl 1107.92044
Summary: The fox-rabies model consists of two nonlinear partial differential equations. In this model the fox population is divided into two species: susceptible \((S)\) and infective \((I)\). Finite-difference methods are used to compute the numerical solution of the initial/boundary-value problem.
MSC:
| 92D30 | Epidemiology |
| 35K57 | Reaction-diffusion equations |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
References:
| [1] | M. R. Abo Elrish,The Numerical Solution of Fox-Rabies Modelling, Ph. D. Thesis, Brunel University 2002. |
| [2] | M. R. Abo Elrish and E. H. Twizell,A second-order Explicit Scheme for The Numerical Solution of A fox-abies Model, Int. J. Computer Maths81 (2004), 1027–1038. · Zbl 1052.92046 · doi:10.1080/03057920412331272117 |
| [3] | G. M. Baer,The Natural History of Rabies Academic Press, New York 1975. |
| [4] | G. A. Gardner, L. R. T. Gardner and J. Cunningham,Simulations of A fox-rabies Epidemic on an Island Using Space-time Finite Elements, Z. Naturforsch45c (1990), 1230–1240. |
| [5] | F. N. M. Al-Showaikh and E. H. Twizell,One-dimensional Measles Dynamics, Applied Mathematics and Computation,152 (2004) 169–194. · Zbl 1047.92040 · doi:10.1016/S0096-3003(03)00554-X |
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