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We propose two disease transmission models: the SI model with di®u-sive terms as a model for transmission of avian in°uenza viruses among °ock withconstant population density, and the host-vector SI model with di®usive terms fortransmission among °ock and human. There is a threshold number that determinewhether the diseases become epidemic or not. It depends on three parameters: theaverage length of the infective period, the contact parameter, and the density ofsusceptible population at the initial time. With di®usive terms in the model, thespatial spread of the infection is obvious. Threshold number greater than one isalso the necessary condition for the spreading of infection in the form of a travelingpulse. Its minimum velocity can be determined. We implement the MacCormackmethod, and simulate the generation of a traveling pulse starting from one infectedbird. Numerically, we obtain the percentage of survival in °ock and human afterthe epidemic. We also simulate the minimal portion of immunization in order toprevent further spread.