International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 805-814

An epidemic model with density dependent parameters and vaccination

Q. J. A. Khan and B. S. Bhatt

Department of Mathematics and Computing, College of Science, Sultan Qaboos University, P O Box 36, Postal Code 123 AI-Khod, Muscat, Oman

Received 29 July 1993; Revised 28 December 1994

Copyright © 1996 Q. J. A. Khan and B. S. Bhatt. 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.


A model originally suggested by Greenhalgh [12] and later modified by that same author [13,14] is considered under the assumption that the transmission coefficient is inversely proportional to the total population size. The purpose of this study is to see the effect of this density dependent transmission coefficient on the stability criteria for the equilibrium of the model equations. It is found that Greenhalgh’s results are still valid.