A Traveling Pulse Behavior of the Spread of the Avian Flu Viruses among Flock and Human

We propose two disease transmission models: the SI model with diffusive terms as a model for transmission of avian influenza viruses among flock with constant population density, and the host-vector SI model with diffusive terms for transmission among flock and human. There is a threshold number that determine whether the diseases become epidemic or not. It depends on three parameters: the average length of the infective period, the contact parameter, and the density of susceptible population at the initial time. With diffusive terms in the model, the spatial spread of the infection is obvious. Threshold number greater than one is also the necessary condition for the spreading of infection in the form of a traveling pulse. Its minimum velocity can be determined. We implement the MacCormack method, and simulate the generation of a traveling pulse starting from one infected bird. Numerically, we obtain the percentage of survival in flock and human after the epidemic. We also simulate the minimal portion of immunization in order to prevent further spread.