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

Wang, Lianwen ^[1] ; Zhang, Xingan ^[2] ; Liu, Zhijun ^[1]
1. [1] Hubei University for Nationalities
  
  Hubei University for Nationalities
  
  China
2. [2] Central China Normal University
  
  Central China Normal University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 2, 2018, págs. 309-329
Idioma: inglés
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Resumen
- 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.