On avian influenza epidemic models with time delay

After the outbreak of the first avian influenza A virus (H5N1) in Hong Kong in 1997, another avian influenza A virus (H7N9) crossed the species barrier in mainland China in 2013 and 2014 and caused more than 400 human cases with a death rate of nearly 40 %. In this paper, we take account of the incubation periods of avian influenza A virus and construct a bird-to-human transmission model with different time delays in the avian and human populations combining the survival probability of the infective avian and human populations at the latent time. By analyzing the dynamical behavior of the model, we obtain a threshold value for the prevalence of avian influenza and investigate local and global asymptotical stability of equilibria of the system.