A delayed avian influenza model with avian slaughter: Stability analysis and optimal control

H7N9 avian influenza, a zoonotic disease caused by the transmission of the avian influenza A virus from poultry to humans, is low pathogenic for poultry but highly pathogenic for humans. Slaughter is an effective way to control the outbreak. In this paper, we consider the slaughter of avian population and the incubation periods of avian influenza A virus, and develop a poultry-to-human epidemiological model including time delays of being infectious for the avian and human populations after infection. By studying the dynamical behavior of this delay model, we obtain a threshold value for the extinction and prevalence of avian influenza, and show the local and global asymptotical properties of the two equilibria of the model. We further choose the slaughter intensity and the effect of education campaign as control variables, and formulate an optimal control problem to minimize the disease outbreak and control cost. We solve the optimal control problem and perform numerical simulations to illustrate the analytical results.