Positive Periodic Solutions of an Epidemic Model with Seasonality

Sun, Gui-Quan; Bai, Zhenguo; Zhang, Zi-Ke; Zhou, Tao; Jin, Zhen

doi:10.1155/2013/470646

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Journal article

Positive Periodic Solutions of an Epidemic Model with Seasonality

Sun, Gui-Quan Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China
Bai, Zhenguo Department of Applied Mathematics, Xidian University, Xi’an, Shaanxi 710071, China
Zhang, Zi-Ke Department of Physics, University of Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland
Zhou, Tao Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
Jin, Zhen School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China

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The Scientific World Journal. - Hindawi Limited. - 2013, vol. 2013, p. 1-10

General Biochemistry, Genetics and Molecular Biology

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 numberRdis obtained. Moreover, only the basic reproduction numberR0cannot ensure the existence of the positive equilibrium, which needs additional conditionRd>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.

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