  The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for
biological control of non-native species. The strategy works by manipulating
the sex ratio of a population through the introduction of \textit{supermales}
that guarantee male offspring. In the current manuscript, we compare the TYC
method with a pure harvesting strategy. We also analyze a hybrid harvesting
model that mirrors the TYC strategy. The dynamic analysis leads to results on
stability, global boundedness of solutions and bifurcations of the model.
Several conclusions about the different strategies are established via optimal
control methods. In particular, the results affirm that either a pure
harvesting or hybrid strategy may work better than the TYC method at
controlling an invasive species population.
