Backward bifurcations in epidemiological models

This paper is about the phenomenological study of bifurcations in epidemiological models, in partic-ular, in backward bifurcation. We consider models that exhibit such bifurcation and also consider the factors that cause them. The phenomenon of backward bifurcation in disease transmission models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated repro-duction number is less than unity, has been observed in a number of disease transmission models. The epidemiological consequence of backward bifurcation is that the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, for disease elimination (hence, the presence of this phenomenon in the transmission dynamics of a disease makes its effective control in the community difficult).

Keywords:

Backward bifurcation , Equilibrium , Reproduction number , Stability