The approach of modification the infectious disease models that allow to investigate small-scale spatially distributed influences on the process development by diffusion perturbation of the corresponding degenerate problems of the model is proposed. The singularly perturbed model problem with time-delay is reduced to a sequence of problems without time-delay and the corresponding representations of asymptotic expansions the solutions are constructed. The results of numerical experiments that characterize the influence of spatially distributed diffusion "redistributions" of infectious disease factors on the development of the process are given. The decrease in the maximum level of pathogenic antigens concentration in the infection locus due to their diffusion "redistribution" is illustrated.