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Periodic culling outperforms isolation and vaccination strategies in controlling Influenza A H5N6 outbreaks in the Philippines

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. In this study, we incorporate half-saturated incidence in our mathematical models and investigate three intervention strategies against H5N6: isolation with treatment, vaccination and modified culling. We determine the direction of the bifurcation when $\mathcal{R}_0 = 1$ and show that all the models exhibit forward bifurcation. We administer 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 a better control strategy in prohibiting an outbreak and avoiding further recurrence of the infection from the population compared to confinement and vaccination.