An SEIR Epidemic Model with Relapse and General Nonlinear Incidence Rate with Application to Media Impact

An SEIR Epidemic Model with Relapse and General Nonlinear Incidence Rate with Application to... The aim of this paper is to extend the incidence rate of an SEIR epidemic model with relapse and varying total population size to a general nonlinear form, which does not only include a wide range of monotonic and concave incidence rates but also takes on some neither monotonic nor concave cases, which may be used to reflect media education or psychological effect. By application of the novel geometric approach based on the third additive compound matrix, we focus on establishing the global stability of the SEIR model. Our analytical results reveal that the model proposed can retain its threshold dynamics that the basic reproduction number completely determines the global stability of equilibria. Our conclusions are applied to two special incidence functions reflecting media impact. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Qualitative Theory of Dynamical Systems Springer Journals

An SEIR Epidemic Model with Relapse and General Nonlinear Incidence Rate with Application to Media Impact

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Mathematics, general; Dynamical Systems and Ergodic Theory; Difference and Functional Equations
ISSN
1575-5460
eISSN
1662-3592
D.O.I.
10.1007/s12346-017-0231-6
Publisher site
See Article on Publisher Site

Abstract

The aim of this paper is to extend the incidence rate of an SEIR epidemic model with relapse and varying total population size to a general nonlinear form, which does not only include a wide range of monotonic and concave incidence rates but also takes on some neither monotonic nor concave cases, which may be used to reflect media education or psychological effect. By application of the novel geometric approach based on the third additive compound matrix, we focus on establishing the global stability of the SEIR model. Our analytical results reveal that the model proposed can retain its threshold dynamics that the basic reproduction number completely determines the global stability of equilibria. Our conclusions are applied to two special incidence functions reflecting media impact.

Journal

Qualitative Theory of Dynamical SystemsSpringer Journals

Published: Feb 21, 2017

References

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