A Basic Backward Bifurcation Model in Epidemiology

Abstract

The existence of a backward bifurcation has important consequences in the strategies and control policies designed to eradicate or control an infectious disease because the policies of public health when this phenomenon appears change from the classically adopted ones. The present work gives a characterization of a big family of models including a wide variety of the models present in the literature which show a backward bifurcation. In addition, it explains how the backward bifurcation can be generated and preserved or eliminated. We define what we call the basic backward bifurcation model, and show that it is contained in all the other models showing a backward bifurcation.