Sun Gui-Quan, Bai Zhenguo, Zhang Zi-Ke, Zhou Tao, Jin Zhen
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.
ScientificWorldJournal. 2013 Nov 10;2013:470646. doi: 10.1155/2013/470646. eCollection 2013.
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.
研究了具有逻辑斯谛增长率的SEI自治模型及其相应的非自治模型。对于自治情形，给出了平衡点的吸引区域并进行了一些数值模拟。得到了基本人口再生产数(R_d)。此外，仅基本再生数(R_0)不能确保正平衡点的存在，这需要附加条件(R_d > R_1)。对于非自治情形，通过引入由谱半径定义的基本再生数，研究了疾病的一致持续性和灭绝性。结果表明，对于周期系统，基本再生数比平均再生数更精确。
