American Institute of Mathematical Sciences

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2009, 6(2): 395-407. doi: 10.3934/mbe.2009.6.395

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

Muntaser Safan 1, and  Klaus Dietz 2,

1. 

Mathematics Department, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
2. 

Department of Medical Biometry, Faculty of Medicine, University of Tuebingen, Westbahnhofstr. 55, 72070 Tuebingen, Germany

Received  May 2008 Revised  July 2008 Published  March 2009

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: local stability, global stability, eradication effort., epidemic model, backward bifurcation, vaccination.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Muntaser Safan, Klaus Dietz. On the eradicability of infections with partially protective vaccination in models with backward bifurcation. Mathematical Biosciences & Engineering, 2009, 6 (2) : 395-407. doi: 10.3934/mbe.2009.6.395
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