Applications of Mathematics

, Volume 57, Issue 6, pp 601-616

First online:

Existence of positive periodic solutions of an SEIR model with periodic coefficients

  • Tailei ZhangAffiliated withSchool of Mathematics and Statistics, Xi’an Jiaotong University Email author 
  • , Junli LiuAffiliated withSchool of Science, Xi’an Polytechnic University
  • , Zhidong TengAffiliated withCollege of Mathematics and System Sciences, Xinjiang University

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An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.


epidemic model coincidence degree Fredholm mapping

MSC 2010

34C25 54H25 92D30