SIR model with vaccination: bifurcation analysis (Q6155154)

The authors study a deterministic susceptible-infected-recovered (SIR) model of infectious diseases epidemiology where the size of the susceptible compartment is assumed to grow logistically, and a proportion \(p\) of susceptible individuals are vaccinated against the disease at birth. They find that the endemic equilibrium of the model undergoes a double zero bifurcation at \((\mathcal{R}_0, p) = (2, A^2/(4m))\), where \(\mathcal{R}_0\) is the basic reproduction number, \(A\) is the carrying capacity of the population, and \(m\) is the birth rate. They also provide local representations of Hopf, transcritical, Belyakov, heteroclinic and saddle-node bifurcation curves. Overall, the results could be interesting to applied mathematicians working in infectious disease epidemiology.