International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 347-355
doi:10.1155/S0161171294000487
An SIRS epidemic model of Japanese Encephalitis
1Department of Community Medicine, Burdwan Medical College, Burdwan 713 104, West Bengal, India
2Embryology Unit, Indian Statistical Institute, Calcutta 700 035, India
Received 3 October 1991; Revised 5 October 1992
Copyright © 1994 B. B. Mukhopadhyay and P. K. Tapaswi. 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.
Abstract
An epidemiological model of the dynamics of Japanese Encephalitis (J.E.) spread coupling the SIRS (Susceptible/Infected/Removal/Susceptible) models of J.E. spread in the reservoir population and in the human population has been proposed. The basic reproductive rate R(0) in the coupled system has been worked out. Using Aron's results (cf. [1] and [2]), it has been observed that the disease-free system is stable in this coupled system also, if R(0) is less than unity, and if R(0) is greater than unity, the disease-free system is unstable and there exists a unique stable endemic equilibrium.
The model also shows that in contrast to Aron's observations, loss of immunity is independent of the rate of exposure to the disease. This observation sheds light on the control measure of J.E. by vaccination. Passive immunization, i.e., administration of antibody at recurrent intervals is the correct method of vaccination to eradicate the disease.