Homoclinic bifurcation in an SIQR model for childhood diseases
The authors study an SIQR model for childhood disease, where \(S, I, Q, R\) denote the number of susceptible, infected, isolated (quarantined) and recovered individuals, respectively. A center manifold reduction at a bifurcation point has the normal form for this model: \[ \dot x=y, \quad \dot y=axy+bx^2y+0(4), \] which indicate that there is a bifurcation of codimension greater than two for some critical parameter values. In particular, the authors find an unfolding which gives rise to a codimension two bifurcation and prove analytically the existence of limit cycles and homoclinic orbits. They also confirm that there exist Hopf and homoclinic bifurcations of the model by several numerical computations.
scientific article; zbMATH DE number 1556506