The no-isola problem for slowly oscillating periodic solutions of Wright's equation

Let $\alpha>\tfrac{\pi}{2}$, and consider the family of slowly oscillating periodic solutions (SOPS) of Wright's equation

$$y'(t)=-\alpha y(t-1)\{1+y(t)\}.$$

An isola is a connected component of the SOPS family that is disconnected from the branch emanating from the Hopf bifurcation at $\alpha=\tfrac{\pi}{2}$. No-isola problem. There are no isolas of SOPS for $\alpha\in(\tfrac{\pi}{2},1.9)$. This is the remaining open part of Jones' uniqueness conjecture after the no-saddle-node-bifurcation part has been resolved.