On the eradicability of infections with partially protective vaccination in models with backward bifurcation

Pages: 395 - 407, Volume 6, Issue 2, April 2009

doi:10.3934/mbe.2009.6.395       Abstract        Full Text (208.0K)

Muntaser Safan - Mathematics Department, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt (email)
Klaus Dietz - Department of Medical Biometry, Faculty of Medicine, University of Tuebingen, Westbahnhofstr. 55, 72070 Tuebingen, Germany (email)

Abstract: The SIS model of Hadeler and Castillo-Chavez [9] with a constant transfer rate of susceptibles into a partially protected state has been modified to take into account vaccination at birth. The model shows backward bifurcation (existence of multiple endemic stationary states) for certain values of parameters. Parameter values ensuring the existence and nonexistence of endemic equilibria have been discussed. Local and global stability of equilibria have been investigated. The minimum effort required to eradicate the infection has been determined.

Keywords:  epidemic model, vaccination, backward bifurcation, local stability, global stability, eradication effort.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: May 2008;      Accepted: July 2008;      Published: March 2009.