摘要
针对私企同部门技术工人再培训问题,构建了动力学模型.分析了技术工人再培训的唯一正平衡点与非负平衡点的局部稳定性和正平衡点的全局稳定性,进一步利用Matlab对相关结果进行拟合验证.
A dynamic model was built for the retraining of technical workers in the private sector. The global stability of the positive equilibrium and the local stability of the non-negative equilibrium and positive equilibrium was obtained for the technical worker retraining, and the relevant results were verified by Matlab.
引文
[1] INABA H. Threshold and Stability Results for an Age-structured Epidemic Model. Math. Biol.,1990, 28:411-413
[2] Kretzschmar M, Jager J C, etc. The Basic Reproduction Ratio R_0 for a Sexually Transmitted Disease in a Pair Formation Model with Two Types of Pairs. Math. Biosci.,1994, 124:181-205
[3]薛颖,熊佐亮.具有免疫接种且总人口规模变化的SIR传染病模型的稳定性.应用泛函分析学报,2007,9(2):71-76(Xue Ying, XIONG Zuoliang. Stability of an SIR Epidemic Model with Vaccinal Immunity and a Varying Total Population Size. Acta Analysis Functionalis Applicata, 2007, 9(2):71-76)
[4]霍海峰,佘玉星,孟新友.一类公共健康教育影响下的戒烟模型的稳定性.兰州理工大学学报,2010,36(3):135-138(HUO Haifeng, SHE Yuxing, MENG Xinyou. Stability of a class of smoking curtailing model accomodated to public health educational campaigns. Journal of Lanzhou University of Technology, 2010,36(3):135-138)
[5] Mukandavire Z, Garira W, Tchuenche J M. Modelling effects of public health educational campaigns on HIV/AIDS trans mission dynamics. Applied Mathematical Modelling, 2009, 33(4):2084-2095
[6]李春艳,李冬梅,尹晓.具有连续预防接种和垂直传染的SIR流行病模型的稳定性分析.黑龙江大学自然科学学报,2009, 26(6):739-741(LI Chunyan, LI Dongmei, YIN Xiao. The stability analysis of the SIR epidemic models with vertical infection and continuous vaccination. Journal of Natural Science of Heilongjiang University, 2009,26(6):739-741)
[7] Agarwalm, Vermav. Stability and Hopf Bifurcation Analysis of a SIRS Epidemic Model with Time Delay. J. of Appl. Math and Mech., 2012, 8(9):1-16
[8] Aiello W G, Freedman H I, Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. J. Appl. Math., 1992, 52(3):855-869
[9] Chen Fengde, Wang Hainan, Lin Yuhua. Global stability of a stage-structured predator-prey system.Int. J. Biomath., 2013, 223(3):45-53
[10] Fred Brauer Carlos Castillo-Chavez.生物数学-种群生物学与传染病学中的数学模型.北京:清华大学出版社,2013, 107-136(Fred Brauer Carlos Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology.Beijing:Tsinghua University Press, 2013, 107-136)
[11]张锦炎,冯贝叶.常微分方程几何理论与分支问题.北京:北京大学出版社,2000:1-177(ZHANG Jinyan, Feng Bei-ye. Geometric Theory and Bifurcation Problem of Ordinary Differential Equation. Beijing:Peking University Press, 2000:1-177)
[12] ZHOU J. An SIS Disease Transmission Model with Recruitment-birth-deat Demo-graphics. Math Comput. Modelling, 1995, 21:1-11
[13]陈兰荪.数学生态学模型与研究方法.北京:科学出版社,1988:391-393(CHENG Lansun. Mathematical Ecology Model and Research Method. Beijing:Science Press, 1988:391-393)
[14]马知恩,周义仓.常微分方程定性与稳定性方法.北京:科学出版社,2001:24-27, 70(MA Zhien, ZHOU Yicang. Qualitative and Stable Methods for Ordinary Differential Equations.Beijing:Science Press, 2001:24-27, 70)
[15] Dieudonne J,郭瑞芝.现代分析基础.北京:科学出版社,1982, 275-276(Dieudonne J, GUO Ruizhi. Basis of Modern Analysis. Beijing:Science Press, 1982, 275-276)
