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Hopf Bifurcation Analysis of a New SEIRS Epidemic Model with Nonlinear Incidence Rate and Nonpermanent Immunity
Joint Authors
Markakis, M. P.
Douris, Panagiotis S.
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-01-17
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
A new SEIRS epidemic model with nonlinear incidence rate and nonpermanent immunity is presented in the present paper.
The fact that the incidence rate per infective individual is given by a nonlinear function and product of rational powers of two state variables, as well as the introduction of an epidemic-induced death rate, leads to a more realistic modeling of the physical problem itself.
A stability analysis is performed and the features of Hopf bifurcation are investigated.
Both the corresponding critical regions in the parameter space and their stability characteristics are presented.
Furthermore, by using algorithms based on a new symbolic form as regards the restriction of an n-dimensional nonlinear parametric system to the center manifold and the normal forms of the corresponding Hopf bifurcation, as well, the associated bifurcation diagram is derived, and finally various emerging limit cycles are numerically obtained by appropriate implemented methods.
American Psychological Association (APA)
Markakis, M. P.& Douris, Panagiotis S.. 2018. Hopf Bifurcation Analysis of a New SEIRS Epidemic Model with Nonlinear Incidence Rate and Nonpermanent Immunity. International Journal of Mathematics and Mathematical Sciences،Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1173434
Modern Language Association (MLA)
Markakis, M. P.& Douris, Panagiotis S.. Hopf Bifurcation Analysis of a New SEIRS Epidemic Model with Nonlinear Incidence Rate and Nonpermanent Immunity. International Journal of Mathematics and Mathematical Sciences No. 2018 (2018), pp.1-13.
https://search.emarefa.net/detail/BIM-1173434
American Medical Association (AMA)
Markakis, M. P.& Douris, Panagiotis S.. Hopf Bifurcation Analysis of a New SEIRS Epidemic Model with Nonlinear Incidence Rate and Nonpermanent Immunity. International Journal of Mathematics and Mathematical Sciences. 2018. Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1173434
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1173434