Role of Frequency-dependent Transmission Function in Vaccine-induced Backward Bifurcation in Some Typhoid Models

Abstract

The phenomenon of backward bifurcation in disease models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity has important implications for disease control. The classical requirement of the reproduction number being less than less unity becomes only a necessary, but not sufficient condition for disease elimination. This paper addresses the role of the choice of density-dependent function in a vaccine-induced backward bifurcation in Typhoid models. This result is independent of the type of vaccination program adopted. These results emphasize the need for further work on the density-dependent functions used in Typhoid models.