Journal article

Positive periodic solutions of an epidemic model with seasonality

  • Sun, Gui-Quan Complex Sciences Center, Shanxi University, Taiyuan, China - School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, China - Department of Mathematics, North University of China, Taiyuan, Shanxi, China
  • Bai, Zhenguo Department of Applied Mathematics, Xidian University, Xi’an, Shaanxi, China
  • Zhang, Zi-Ke Institute of Information Economy, Hangzhou Normal University, Hangzhou, China - Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan, China - Department of Physics, University of Fribourg, Switzerland
  • Zhou, Tao Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan, China
  • Jin, Zhen Complex Sciences Center, Shanxi University, Taiyuan, China - School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, China
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    10.11.2013
Published in:
  • The Scientific World Journal. - 2013, vol. 2013
English An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction Rd number is obtained. Moreover, only the basic reproduction number R0 cannot ensure the existence of the positive equilibrium, which needs additional condition Rd > R1. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number.
Faculty
Faculté des sciences
Department
Physique
Language
  • English
Classification
Physics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/303496
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