SIR Model with Vaccination: Bifurcation Analysis

Abstract There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a model where class Susceptible individuals grows logistically has been subject to constant vaccination. We explicitly prove endemic equilibrium is codimension two singularity parameter space $$(\mathcal {R}_0, p)$$ ( R 0 , p ) , $$\mathcal {R}_0$$ basic reproduction number p proportion successfully vaccinated at birth. exhibit Hopf transcritical Belyakov heteroclinic saddle-node bifurcation curves unfolding . The parameters written useful way evaluate necessary eliminate disease conclude how may affect outcome epidemic. also region persists illustrate our main result with numerical simulations, emphasizing role parameters.