Qualitative Theory of Dynamical Systems

, Volume 17, Issue 2, pp 309–329 | Cite as

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

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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.

Keywords

General nonlinear incidence rate Relapse Media impact Global stability Varying total population size 

Mathematics Subject Classfication

34D23 92D30 
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Notes

Acknowledgements

The authors thank the editor and the anonymous reviewers for their constructive comments and valuable suggestions which help us to greatly improve the presentation of this paper. The work is supported by National Natural Science Foundation of China (Nos.11371161 and 11261017). The work is also sponsored by Youth Talents Project of Science and Technology Research Plan of Hubei Provincial Education Department, and Doctoral Scientific Research Starting Found of Hubei University for Nationalities.

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of MathematicsHubei University for NationalitiesEnshiChina
  2. 2.School of Mathematics and StatisticsCentral China Normal UniversityWuhanChina

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