The emerging threat of a human pandemic caused by high-pathogenic H5N1 avian inuenza virus magnifies the need for controlling the incidence of H5N1 in domestic bird populations. The two most widely used control measures in poultry are culling and vaccination. In this talk, I will discuss mathematical models of avian influenza in poultry which incorporate culling and vaccination. First, we consider an ODE model to understand the dynamics of avian influenza under different culling approaches. Under certain conditions, complex dynamical behavior such as bistability is observed and analyzed. Next, we model vaccination of poultry by formulating a coupled hybrid ODE-PDE model which takes into account vaccine-induced asymptomatic infection. In this study, the model can exhibit the "silent spread" of the disease through asymptomatic infection. We analytically and numerically demonstrate that vaccination can paradoxically increase the total number of infected when the efficacy is not sufficiently high.