Abstract: A mathematical model describing the interaction between virus and antibody was studied. The authors modified the origional model first by replacing the Laplacian in the origional model with a nonlinear p-Laplacianoperator and then proved the existence and uniqueness of the weak solutions to the model. Also, the authors studied the limit behavior　of the solution as the reaction rate tended to infinity. The result obtaind coincides with the case one can observe.

Key words: fast reaction, nonlinear diffusion, p-Laplacian