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Partial Differential Equations of an Epidemic Model with Spatial Diffusion
Joint Authors
Yousfi, Noura
Maziane, Mehdi
Lotfi, El Mehdi
Hattaf, Khalid
Source
International Journal of Partial Differential Equations
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-10
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate.
The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved.
The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations.
By means of Lyapunov functional, the global stability of both equilibria is investigated.
More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the eradication of disease from population.
When the basic reproduction number is greater than unity, then disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable; in this case the disease persists in the population.
Numerical simulations are presented to illustrate our theoretical results.
American Psychological Association (APA)
Lotfi, El Mehdi& Maziane, Mehdi& Hattaf, Khalid& Yousfi, Noura. 2014. Partial Differential Equations of an Epidemic Model with Spatial Diffusion. International Journal of Partial Differential Equations،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-452886
Modern Language Association (MLA)
Lotfi, El Mehdi…[et al.]. Partial Differential Equations of an Epidemic Model with Spatial Diffusion. International Journal of Partial Differential Equations No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-452886
American Medical Association (AMA)
Lotfi, El Mehdi& Maziane, Mehdi& Hattaf, Khalid& Yousfi, Noura. Partial Differential Equations of an Epidemic Model with Spatial Diffusion. International Journal of Partial Differential Equations. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-452886
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-452886