  The Trojan Y Chromosome (TYC) Strategy is a promising eradication method that
attempts to manipulate the female to male ratio to promote the reduction of the
population of an invasive species. The manipulation stems from an introduction
of sex-reversed males, called supermales, into an ecosystem. The offspring of
the supermales is guaranteed to be male. Mathematical models have shown that
the population can be driven to extinction with a continuous supply of
supermales. In this paper, a new model of the TYC strategy is introduced and
analyzed that includes two important modeling characteristics, that are
neglected in all previous models. First, the new model includes intraspecies
competition for mates. Second, a strong Allee effect is included. Several
conclusions about the strategy via optimal control are established. These
results have large scale implications for the biological control of invasive
species.
