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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 
 
 

Content
 

Volumes > Volume 19 > No. 3

 
   

Stability properties of an epidemic model with cross-diffusion

PP: 541-549
doi:10.18576/amis/190306
Author(s)
A. A. Soliman, Manar M. Dahshan, Ahmed S. Elgazzar,
Abstract
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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