Salem Abdelmalek, Samir Bendoukha
In this article, we consider a spatially SVIR model of infectious disease epidemics which allows for continuous immigration of all classes of individuals. We show that the proposed model has a unique steady state that is asymptotically stable. Using an appropriately constructed Lyapunov functional, we establish its global asymptotic stability. Numerical results obtained through Matlab simulations are presented to confirm the results.
Submitted May 10, 2016. Published October 24, 2016.
Math Subject Classifications: 35K45, 35K57.
Key Words: Reaction diffusion systems; SVIR; immigration; Lyapunov functional; large time behavior.
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| Salem Abdelmalek |
Department of mathematics
University of Tebessa 12002, Algeria
| Samir Bendoukha |
Electrical Engineering Department
College of Engineering at Yanbu
Taibah University, Saudi Arabia
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