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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (5): 10-17.doi: 10.6040/j.issn.1671-9352.0.2016.531

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一类具有不同发生率的双疾病随机SIS传染病模型的动力学研究

张道祥1,2,胡伟1,陶龙1,周文1   

  1. 1.安徽师范大学数学计算机科学学院, 安徽 芜湖 241002;2.赫尔辛基大学数理统计学院, 芬兰 赫尔辛基 00014
  • 收稿日期:2016-11-18 出版日期:2017-05-20 发布日期:2017-05-15
  • 作者简介:张道祥(1979— ),男,博士,副教授,研究方向为微分方程理论及其应用. E-mail:18955302433@163.com
  • 基金资助:
    国家自然科学基金青年项目(11302002)

Dynamics of a stochastic SIS epidemic model with different incidences and double epidemic hypothesis

ZHANG Dao-xiang1,2, HU Wei1, TAO Long1, ZHOU Wen1   

  1. 1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China;
    2. Department of Mathematics and Statistics, University of Helsinki, Helsinki 00014, Finland
  • Received:2016-11-18 Online:2017-05-20 Published:2017-05-15

摘要: 提出了一类新的具有不同发生率的双疾病随机SIS传染病模型。 借助Lyapunov函数和伊藤公式, 获得了模型中疾病的灭绝以及系统持久性的充分条件。 结果表明不仅强噪声能够使得传染病灭绝,而且弱噪声在一定条件下也能使传染病灭绝。

关键词: 随机传染病模型, 阈值, 持久性, 灭绝性

Abstract: We propose a new mathematical model with two different incidence rates and double epidemic hypothesis. By the Lyapunov function and Itôs formula, we explore and obtain the threshold of a stochastic SIS system for the extinction and thepermanence in mean of two epidemic diseases. The results show that not only a large stochastic disturbance but also a small stochastic disturbance can cause infectious diseases to go to extinction.

Key words: stochastic epidemic model, extinction, threshold, permanence

中图分类号: 

  • Q332
[1] 马知恩, 周义仓, 王稳地, 等. 传染病动力学的数学建模与研究[M]. 北京:科学出版社, 2004. MA Zhien, ZHOU Yicang, WANG Wendi, et al. Mathematical modeling and research of infectious diease dynamics[M]. Beijing: Science Press, 2004.
[2] 张道祥, 丁伟伟. 具非连续收获策略的Gilpin-Ayala竞争系统周期解的存在性[J]. 安徽师范大学学报(自然科学版), 2014, 37(6):515-519. ZHANG Daoxiang, DING Weiwei. Existence of periodic solutions of gilpin-ayala competitive system with discontinuous harvesting[J]. Journal of Anhui Normal University(Natural Science), 2014, 37(6):515-519.
[3] GREENHALGH D, AKHAN Q J, Lewis F I. Recurrent epidemic cycles in an infectious disease model with a time delay in loss of vaccine immunity[J]. Nonlinear Anal, 2005, 63:779-788.
[4] KERMAC W O, MCKENDRICK A G. Contributions to the mathematical theory of epidemic[J]. Proceedings of the Royal Society, 1932, A138:55-83.
[5] CHEN Q L, TENG Z D, WANG L, et al. The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence[J]. Nonlinear Dynam, 2013, 719(1/2):55-73.
[6] KUNIYA T, INABA H. Endemic threshold results for an age-structured SIS epidemic model with periodic parameters[J]. J Math Anal Appl, 2013, 402(2):477-492.
[7] LI X Z, LI W S, GOHOS M. Stability and bifurcation of an SIS epidemic model with treatment[J]. Chaos Solitons Fractals, 2009, 42(5):2822-2832.
[8] ZHANG X, LIU X. Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment[J]. Nonlinear Anal, 2009, 10(2):565-575.
[9] GRAY A, GREENHALGH D, HU L, et al. A stochastic differential equation SIS epidemic model[J]. SIAM J Appl Math, 2001, 71(3):876-902.
[10] ZHAO Y N, JIANG D Q, REGAN D O. The extinction and persistence of stochastic SIS epidemic model with Vaccination[J]. Phy A, 2013, 392(20):4916-4927.
[11] LIN Y G, JIANG D Q, WANG S. Stationary distribution of a stochastic SIS epidemic model with Vaccination[J]. Phy A: Statistical Mechanics and its Applications, 2014, 394(2):187-197.
[12] 周艳丽, 张卫国. 非线性传染率的随机SIS传染病模型的持久性和灭绝性[J]. 山东大学学报(理学版), 2013, 48(10): 68-77. ZHOU Yanli, ZHANG Weiguo. Persistence and extinction in stochastic SIS epidemic model with nonlinear incidence rate[J]. Journal of Shandong University(Natural Science), 2013, 48(10):68-77.
[13] MENG X Z, ZHAO S N, FENG T, et al. Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis[J]. J Math Anal Appl, 2016, 433(1):227-242.
[14] XIAO D, RUAN S. Global analysis of an epidemic model with nonmonotone incidence rate[J]. Math Biosci, 2007, 208(2):419-429.
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