AAM  >> Vol. 2 No. 2 (May 2013)

    Epidemic Model with Vertical Transmission and Pulse Vaccination and Non-Monotonic Incidence Rate

  • 全文下载: PDF(246KB) HTML    PP.65-73   DOI: 10.12677/AAM.2013.22009  
  • 下载量: 2,170  浏览量: 7,726  


洪凤玲,王 霞,闫卫平:山西大学数学科学学院,太原

SIRS型传染病模型非单调发病率脉冲免疫垂直传染全局渐近稳定 SIRS Epidemic Model; Non-Monotone Incidence Rate; Impulsive Vaccination; Vertical Transmission; Globally Asymptotically Stable



In this paper, we investigate an SIRS epidemic model with vertical transmission and pulse vaccination and non-monotonic incidence rate. First, we obtain the condition for which the disease-free periodic solution of the epidemic model is globally asymptotically stable when and by Floquet theorem, impulsive comparison theorem and iteration method. Second, permanence of this system is presented by comparison theorem.

洪凤玲, 王霞, 闫卫平. 垂直传染脉冲免疫以及非单调发病率的传染病模型[J]. 应用数学进展, 2013, 2(2): 65-73. http://dx.doi.org/10.12677/AAM.2013.22009


[1] H.-F. Huo, Z.-P. Ma. Dynamics of a delayed epidemic model with non-monotonic incidence rate. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(2): 459-486.
[2] Y. Muroya, Y. Enatsu and Y. Nakata. Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate. Journal of Mathematical Analysis and Applications, 2011, 377(1): 1-14.
[3] R. Xu, Z. E. Ma. Global stability of a SIR epidemic model with nonlinear incidence rate and time delay. Nonlinear Analysis: Real World Applications, 2009, 10(5): 3175-3189.
[4] D. M. Xiao, S. G. Ruan. Global analysis of an epidemic model with nonmonotone incidence rate. Mathematical Biosciences, 2007, 208(2): 419-429.
[5] B. Shulgin, L. Stone and Z. Agur. Pulse vaccination strategy in the SIR epidemic model. Bulletin of Mathematical Biology, 1998, 60(6): 1123- 1148.
[6] L. Stone, B. Shulgin and Z. Agur. Theoretical examination of the pulse vaccination policy in the SIR epidemic model. Mathematical and Computer Modelling, 2000, 31(4-5): 207-215.
[7] S. J. Gao, L. S. Chen, J. J. Nieto and A. Torres. Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine, 2006, 24(35-36): 6037-6045.
[8] Y. C. Zhou, H. W. Lin. Stability of periodic solutions for an SIR model with pulse vaccination. Mathematical and Computer Modelling, 2003, 38: 299-308.
[9] Y. Song. Asymptotical behavior of SIR epidemic models with vertical transmission and Impulsive Vaccination. International Conference on Computer Application and System Modeling (ICCASM2010), Taiyuan, 22-24 October 2010: V1-92-V1-95.
[10] X. B. Zhang, H. F. Huo, H. Xiang and X. Y. Meng. An SIRS epidemic model with pulse vaccination and non-monotonic incidence rate. Nonlinear Analysis: Hybrid Systems, 2013, 8: 13-21.