Modeling the Influence of Small-Scale Diffusion Perturbations on the Development of Infectious Diseases under Immunotherapy

Abstract

The article proposes a modification of the mathematical model of the immunotherapy influence on the immune response dynamics taking into account small-scale diffusion perturbations. The solution of the corresponding singularly perturbed model problem with time-delay is reduced to a sequence of solutions without time-delay, for that representations of the required functions in the form of asymptotic series as disturbances of solutions of the corresponding degenerate problems are constructed. We present the results of numerical modeling that illustrate the influence of diffusion redistribution of active factors on the infectious disease dynamics in the conditions of immunotherapy. The decrease in the level of the maximum concentration of antigens in the locus of infection as a result of their diffusion redistribution is illustrated.