一类具有震动恢复率和时滞的传染病模型的指数收敛性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (5): 987-994.

一类具有震动恢复率和时滞的传染病模型的指数收敛性

许艳丽

湘南学院数学与金融学院湖南郴州 423000

收稿日期:2014-11-19 修回日期:2015-02-18 出版日期:2015-10-25 发布日期:2015-10-25
作者简介:许艳丽,xuyanliling@aliyun.com
基金资助:
国家自然科学基金(11471278)、湖南省自然科学基金(14JJ2133)和湖南省重点建设学科基金资助

Exponential Convergence of An Epidemic Model with Delays and Oscillating Recovery Rates

Xu Yanli

School of mathematics and Finance, Xiangnan University, Hunan Chenzhou 423000

Received:2014-11-19 Revised:2015-02-18 Online:2015-10-25 Published:2015-10-25

摘要/Abstract

摘要：

考虑了一类具有震动恢复率和时滞的传染病模型,建立了使模型所有解指数收敛于零向量的一些充分条件,并用数值模拟验证了所得的结论,改进和推广了已有文献的相应结果.

关键词: 传染病模型, 指数收敛, 时滞, 震动恢复率

Abstract:

This paper is concerned with an epidemic model with delays and oscillating recovery rates. Some new sufficient conditions are established to ensure that all solutions of this model converge exponentially to zero vector. Some numerical simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies.

Key words: Epidemic model, Exponential convergence, Delay, Oscillating recovery rate

中图分类号:

O175.12

许艳丽. 一类具有震动恢复率和时滞的传染病模型的指数收敛性[J]. 数学物理学报, 2015, 35(5): 987-994.

Xu Yanli. Exponential Convergence of An Epidemic Model with Delays and Oscillating Recovery Rates[J]. Acta mathematica scientia,Series A, 2015, 35(5): 987-994.

参考文献

[1] Zhang X, Chen L. The periodic solution of a class of epidemic models. Comput Math Appl, 1999, 38(3/4):61-71
[2] Lajmanovich A, Yorke T A. Adeterministic model for gonorrhea in a nonhomogeneous populaton. Math Biosci, 1976, 28:221-236
[3] Aronsson G, Mellander I. Adeterministic model in biomathematics, asymptotic behavior and threshold conditions. Math Biosci, 1980, 49:207-222
[4] Busenberg S, Cooke K L. Periodic solution of a periodic nonlinear delay differential equation. SIAM J Appl Math, 1978, 35:704-721
[5] Ruan S, Wang W, Levin S A. The effect of global travel on the spread of SARS. Math Biosci, 2006, 3:205-218
[6] Chen L, Sun J. The positive periodic solution for an epidemic model. J Sys Sci Math Sci, 2006, 26(4):456-466
[7] Chen L. The positive periodic solution for a class of nonlinear system with continuous time delay. Math in Prac Theory, 2006, 36(4):151-157
[8] Mukandavire Z, Garira W, Chiyaka C. Asymptotic properties of an HIV/AIDS model with a time delay. J Math Anal Appl, 2007, 330(2):834-852
[9] Zhang F, Zhao X. A periodic epidemic model in a patchy environment. J Math Anal Appl, 2007, 325(1):496-516
[10] d'Onofrio A. Stability properties of pulse vaccination strategy in SEIR epidemic model. Math Biosc, 2002, 26(4):57-72
[11] Smith H L. An Introduction to Delay Differential Equations with Applications to the Life Sciences. New York:Springer, 2011
[12] Wang W. Exponential extinction of Nicholson's blowflies system with nonlinear density-dependent mortality terms. Abstr Appl Anal, 2012, Article ID 302065, 15 pages
[13] Chen Z. A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput & Applic, 2013, 23:2429-2434
[14] Yi X, Gong S, Wang L. Global exponential convergence of an epidemic model with time-varying delays. Nonlinear Anal Real World Appl, 2011, 12(1):450-454
[15] Xiao B, Liu B. Exponential convergence of an epidemic model with continuously distributed delays. Math Comput Model, 2008, 48(3/4):541-547
[16] Zhao C, Yang M. Peng G. Exponential convergence of an epidemic model with time-varying delays. Nonlinear Anal Real World Appl, 2010, 11(1):117-121
[17] Berezansky L, Braverman E. On exponential stability of a linear delay differential equation with an oscillating coefficient. Applied Mathematics Letters, 2009, 22:1833-1837
[18] Hale J K, Kato J. Phase space for retarded equations with infinite delay. Funkcialaj Ekvaci, 1978, 21:11-41