Journal of Applied Mathematics
Volume 2005 (2005), Issue 4, Pages 301-319

Stability on coupling SIR epidemic model with vaccination

Helong Liu,1,2 Houbao Xu,3 Jingyuan Yu,2 and Guangtian Zhu4

1Department of Mathematics, Xinyang Normal University, Henan, Xinyang 464000, China
2Beijing Institute of Information and Control, Beijing 100037, China
3Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
4Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China

Received 9 December 2004; Revised 21 September 2005

Copyright © 2005 Helong Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a mathematical model for the disease which can be transmitted via vector and through blood transfusion in host population. The host population is structured by the chronological age. We assume that the instantaneous death and infection rates depend on the age. Applying semigroup theory and so forth, we investigate the existence of equilibria. We also discuss local stability of steady states.