title: Positive periodic solutions of an epidemic model with seasonality.
abstract: 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 number R d is obtained. Moreover, only the basic reproduction number R 0 cannot ensure the existence of the positive equilibrium, which needs additional condition R d > R 1. 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.
authors: Complex Sciences Center, Shanxi University, Taiyuan 030006, China ; School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China ; Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China.
authors: Gui-Quan
authors: GQ
authors: Sun
authors: Zhenguo
authors: Z
authors: Bai
authors: Zi-Ke
authors: ZK
authors: Zhang
authors: Tao
authors: T
authors: Zhou
authors: Zhen
authors: Z
authors: Jin
mesh_terms: D050936:Basic Reproduction Number / Q000706:statistics & numerical data; D003141:Communicable Diseases / Q000453:epidemiology; D058872:Epidemics / Q000706:statistics & numerical data*; D004813:Epidemiology / Q000706:statistics & numerical data; D006801:Humans; D008433:Mathematics; D015233:Models, Statistical; D011158:Population Growth; D012621:Seasons; D013997:Time Factors