ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

A Generalized Reaction-Diffusion Epidemic Model with Time Delay

Discontinuity, Nonlinearity, and Complexity 9(2) (2020) 217--228 | 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 M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco

$^{2}$ Ibn Zohr University, CST Campus Universitaire Ait Melloul Agadir, Morocco

Abstract

In this paper, we propose a generalized reaction-diffusion 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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