TRAVELING WAVES FOR A SIMPLE DIFFUSIVE EPIDEMIC MODEL

We investigate the existence of traveling wave solutions for the infective-susceptible two-component epidemic model. The model system is described by reaction-diffusion equations with the nonlinear reaction term of the classical Kermack-McKendric type. The diffusion coefficients of infectives and susceptibles are assumed to be positive constants d(1) and d(2) respectively. By the shooting argument with the aid of the invariant manifold theory, we prove that there exists a positive constant c* such that the traveling wave solutions exist for any c greater than or equal to c*. The minimal wave speed c* is shown to be independent of d(2) and to have the same value as that for d(2) = 0.