OJAppS  Vol.2 No.4 B , December 2012
Global stability for delay SIR epidemic model with vertical transmission
Author(s) Junli Liu*, Tailei Zhang
A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamics: if, there only exists the disease-free equilibrium which is globally asymptotically stable; if, there is a unique endemic equilibrium and the disease persists, sufficient cond- itions are obtained for the global asymptotic stability of the endemic equilibrium.

Cite this paper
nullLiu, J. and Zhang, T. (2012) Global stability for delay SIR epidemic model with vertical transmission. Open Journal of Applied Sciences, 2, 1-4. doi: 10.4236/ojapps.2012.24B001.
[1]   K. L. Cooke, Stability analysis for a vector disease model, Rocky Mountain J. Math., vol. 9, 1979, pp. 31-42.

[2]   M. Y. Li, J. S. Muldowney, Global stability for the SEIR model in epidemiology, Math. Biosci., vol.125, 1995, pp. 155-168.

[3]   J. Zhang, Z. E. Ma, Gobal dynamics of an SEIR epidemic moel with saturating contact rate, Mathy. Biosci., vol.185, 2003, pp. 15-32.

[4]   R. Xu, Z. E. Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal. Real World Appli., vol. 10, 2009, pp. 3175-3189.

[5]   X. L. Hu, F. G. Sun and C. X. Wang, Global analysis of SIR epidemic model with the aturated contact rate and vertical transmission, Basic Sciences Journal of Textile Universities, vol.23, 2010, pp. 120-122.

[6]   Y. N. Xiao and L. S. Chen, Modeling and analysis of a predator-prey model with disease in the prey}, Math. Biosci., vol.171, 2001, pp. 59-82.

[7]   Y. Kuang, Delay differential equations with applications in population dynamics, Boston: Academic Press, 1993.

[8]   J. L. Liu, T. L. Zhang, J. X. Lu, An impulsive controlled eco-epidemic model with disease in the prey, J. Appl. Math. Comput., to appear.