  In this paper, we first derive Milstein schemes for an interacting particle
system associated with point delay McKean-Vlasov stochastic differential
equations (McKean-Vlasov SDEs), possibly with a drift term exhibiting
super-linear growth in the state component. We prove strong convergence of
order one and moment stability, making use of techniques from variational
calculus on the space of probability measures with finite second order moments.
Then, we introduce an antithetic multilevel Milstein scheme, which leads to
optimal complexity estimators for expected functionals of solutions to delay
McKean-Vlasov equations without the need to simulate L\'evy areas.
