Highly Pathogenic Avian Influenza A (H5N6) is a mutated virus of Influenza A (H5N1) and a new emerging infection that recently caused an outbreak in the Philippines. The 2017 H5N6 outbreak resulted in a depopulation of 667,184 domestic birds. We incorporate half-saturated incidence and optimal control in our mathematical models in order to investigate three intervention strategies against H5N6: isolation with treatment, vaccination, and modified culling. We determine the direction of the bifurcation when R0=1 and show that all the models exhibit forward bifurcation. We apply the theory of optimal control and perform numerical simulations to compare the consequences and implementation cost of utilizing different intervention strategies in the poultry population. Despite the challenges of applying each control strategy, we show that culling both infected and susceptible birds is an effective control strategy in limiting an outbreak, with a consequence of losing a large number of birds; the isolation-treatment strategy has the potential to prevent an outbreak, but it highly depends on rapid isolation and successful treatment used; while vaccination alone is not enough to control the outbreak.