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Stability properties of an epidemic model with cross-diffusion |
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PP: 541-549 |
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doi:10.18576/amis/190306
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Author(s) |
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A. A. Soliman,
Manar M. Dahshan,
Ahmed S. Elgazzar,
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Abstract |
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| Mathematical models play a crucial role in understanding the dynamics of epidemics. Reaction-diffusion systems provide a powerful framework for modeling epidemics. We study a spatio-temporal SI epidemic model that includes both self-diffusion and cross-diffusion. The basic reproductive ratio is calculated. The asymptotic stability and Turing instability of both disease-free and endemic equilibria are investigated. We found that the stability properties of both equilibria are preserved in the diffusive model. We investigate the dynamics of the model numerically using a finite difference scheme. We perform numerical simulations for different parameter settings. The simulation results are consistent with the analytical study.
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