On the backward bifurcation of a vaccination model with nonlinear incidence - Buonomo, B.; Lacitignola, D. (Nonlinear Analysis: Modelling and Control, 2011)
A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced in [2], which is based on the use of the center manifold theory. Conditions ensuring the occurrence of backward bifurcation are derived. The obtained results are numerically validated and then discussed from both the mathematical and the epidemiological perspective.
Keywords: epidemic models; backward bifurcation; disease control; nonlinear incidence; vaccination