|本期目录/Table of Contents|

[1]王青,路秋英.带有饱和发生率和线性饱和治疗函数的SIS模型的动力学研究[J].浙江理工大学学报,2018,39-40(自科5):630-636.
 WANG Qing,LU Qiuying.Research on dynamical behaviors of SIS epidemic model with saturation incidence and linear saturation therapy function[J].Journal of Zhejiang Sci-Tech University,2018,39-40(自科5):630-636.
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带有饱和发生率和线性饱和治疗函数的SIS模型的动力学研究()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第39-40卷
期数:
2018年自科5期
页码:
630-636
栏目:
出版日期:
2018-08-31

文章信息/Info

Title:
Research on dynamical behaviors of SIS epidemic model with saturation incidence and linear saturation therapy function
文章编号:
1673-3851 (2018) 09-0630-07
作者:
王青路秋英
浙江理工大学理学院,杭州 310018
Author(s):
WANG Qing LU Qiuying
School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
治疗函数SIS传染病模型后向分支平衡点
分类号:
O193
文献标志码:
A
摘要:
改进了一类具有饱和发生率和不具有常态预防的饱和治疗函数的传染病模型,改进后的模型具有常态预防能力,更能反映真实的传染病防治情况,所得结论更具一般性。利用定性理论和稳定性分析,研究了模型的平衡点个数、平衡点的稳定性以及后向分支问题。研究发现:模型最多存在4个平衡点;当基本再生数小于1时,若饱和治疗率较小,常态预防能力较大或者过早采取最大治疗能力,模型发生后向分支。

参考文献/References:

[1] Kermack W O, Mckendrick A G.A contribution to the mathematical theory of epidemics [J]. Proceedings of the Royal Society of London Series A, 1927, 115:700-721.
[2] Wei J J, Cui J A. Dynamics of SIS epidemic model with the standard incidence rate and saturated treatment function [J].International Journal of Biomathematics, 2012, 5(3):1-18.
[3] Hu Z X, Liu S, Wang H. Backward bifurcation of an epidemic model with standard incidence rate and treatment rate [J].Nonlinear Mathematical Real World Applications, 2008, 9(5):2302-2312.
[4] Capasso V, Serio G.A generalization of the KermackMckendrick deterministic epidemic model [J]. Mathematical  Biosciences, 1978, 42:43-75.
[5] 吴琼,滕志东.一类具有饱和发生率和治疗的SIS传染病模型的后向分支及动力学行为[J].新疆大学学报(自然科学版),2014,31(2):174-180.
[6] 周康, 路秋英.带有线性饱和治疗函数的SIR模型动力学研究[J].浙江理工大学学报,2017,37(6):874-880.
[7] Khan MA, Khan Y, Islam S. Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment [J]. Physica AStatistical Mechanics and Its Applications, 2018(493):210-227.
[8] Zhou T T, Zhang W P, Lu Q Y. Bifurcation analysis of an SIS epidemic model with saturated incidence rate and saturated treatment function [J].Applied Mathematics and Computation, 2014, 226(1):288-305.
[9] Xiao D M, Ruan S G. Global analysis of an epidemic  model with nonmonotone incidence rate [J].Mathematical  Biosciences, 2007, 208(2):419-429.
[10] Ruan S G, Wang W D. Dynamical behavior of an epidemic model with a nonlinear incidence rate [J].Journal of Differential Equations, 2003, 188(1):135-163.

相似文献/References:

[1]周康,路秋英.带有线性饱和治疗函数的SIR-模型动力学研究[J].浙江理工大学学报,2017,37-38(自科6):874.
 ZHOU Kang,LU Qiuying.Research on Dynamical Behaviors of  SIR Epidemic Model with Linear Saturation Therapy Function[J].Journal of Zhejiang Sci-Tech University,2017,37-38(自科5):874.

备注/Memo

备注/Memo:
收稿日期: 2018-03-28
网络出版日期: 2018-05-03
作者简介: 王青(1992-),女,安徽安庆人,硕士研究生,主要从事常微分方程与动力系统的研究
通信作者: 路秋英,E-mail:qiuyinglu@163.com
更新日期/Last Update: 2018-09-12