“…It follows that (Y (a) −Ȳ (a)) and M ∂ a y (t, a) are collinear, which yields(20). Moreover, Y (a) − M y (t, a) andȲ (a) − Mȳ(t, a) are also collinear and consequently(21) holds.In the second case, (16) yields βI(t − a)( X(a) − y(t, a)) = 0. It can be easily checked that when starting from a positive infected population at time zero, I remains positive on [0, T ], so X(a) = y(t, a) =X(a).…”