TRAVELING WAVES FOR A SIMPLE DIFFUSIVE EPIDEMIC MODEL

Source abstract

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≥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.