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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article
journalArticle
Université de Fribourg
Fribourg
eng
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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.
53
http://dx.doi.org/10.1155/2013/470646
The Scientific World Journal
2013/2013//-
http://doc.rero.ch/record/209595/files/zha_pps.pdf
http://doc.rero.ch/record/209595/files/zha_pps.pdf
http://doc.rero.ch/record/209595
20150420164653.0
209595