Discontinuity, Nonlinearity, and Complexity
A Generalized ReactionDiffusion Epidemic Model with Time Delay
Discontinuity, Nonlinearity, and Complexity 9(2) (2020) 217228  DOI:10.5890/DNC.2020.06.004
El Mehdi Lotfi$^{1}$, Radoune Yafia$^{2}$, Noura Yousfi$^{1}$
$^{1}$ Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben Mâ€™sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco
$^{2}$ Ibn Zohr University, CST Campus Universitaire Ait Melloul Agadir, Morocco
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Abstract
In this paper, we propose a generalized reactiondiffusion epidemic model with time delay. The proposed model is governed by partial differential equations (PDEs). The global existence, positivity and boundedness of solutions are obtained. By analyzing the corresponding characteristic equation and constructing appropriate Lyapunov functionals, the local/global stability of homogeneous steady states are investigated. Finally, an application of our analytical results is given.
Acknowledgments
We would like to express our gratitude to the editor and the two anonymous reviewers for their constructive comments and suggestions, which helped us to enrich this paper.
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