Mechanisms contributing to the spread of avian influenza seem to be well identified, but how their interplay led to the current worldwide spread pattern of H5N1 influenza is still unknown due to the lack of effective global surveillance and relevant data. Here we develop some deterministic models based on the transmission cycle and modes of H5N1 and focusing on the interaction among poultry, wild birds and environment. Some of the model parameters are obtained from existing literatures, and others are allowed to vary in order to assess the effectiveness of various control strategies involving bird migration, agro-ecological environments, live and dead poultry trading, smuggling of wild birds, mechanical movement of infected materials and specific farming practices. Our simulations are carried out for a set of parameters that leads to the basic reproduction number 3.3. We show that by reducing 95% of the initial susceptible poultry population or by killing all infected poultry birds within one day, one may control the disease outbreak in a local setting. Our simulation shows that cleaning the environment is also a feasible and useful control measure, but culling wild birds and destroying their habitat are ineffective control measures. We use a one dimensional PDE model to examine the contribution to the spatial spread rate by the size of the susceptible poultry birds, the diffusion rates of the wild birds and the virus. We notice the diffusion rate of the wild birds with high mortality has very little impact on the spread speed. But for the wild birds who can survive the infection, depending on the direction of convection, their diffusion rate can substantially increase the spread rate, indicating a significant role of the migration of these type of wild birds in the spread of the disease.