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BACKWARD BIFURCATION IN A DISCRETE SIS MODEL WITH VACCINATION

SOPHIA R.-J. JANG

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA

Current address: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA. Tel: (+1) 806-742-2566.

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https://doi.org/10.1142/S0218339008002630Cited by:10 (Source: Crossref)

Abstract

A simple discrete SIS model with vaccination is proposed. Its dynamics depend on a lumped parameter R_vac. The model exhibits the classical threshold behavior when vaccination is totally ineffective. When vaccination is partially effective, a backward transcritical bifurcation may occur at R_vac = 1. In this case, the model also undergoes a saddle–node bifurcation at certain parameter values when R_vac < 1. The disease can persist for R_vac > 1 and can be eradicated for R_vac < 1 if a forward transcritical bifurcation occurs at R_vac = 1. However, the disease may persist even when R_vac < 1 if a backward bifurcation occurs at R_vac = 1.

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