Homoclinic bifurcation in an SIQR model for childhood diseases

We consider a system of ODEs which describes the transmission dynamics of c hildhood diseases. A center manifold reduction at a bifurcation point has t he normal form x' = y, y' = axy + bx(2)y + O(4), indicating a bifurcation o f codimension greater than two. A three-parameter unfolding of the normal f orm is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biologi cal considerations. It is shown that the perturbed system produces homoclin ic bifurcation. (C) 2000 Academic Press.