DECISION MAKING IN MODELING THE DYNAMICS OF INFECTIOUS DISEASE TAKING INTO ACCOUNT DIFFUSION DISTURBANCES AND CONCENTRATED ACTIONS

To study the patterns of response of the immune system to viruses detected in the body, a very diverse range of models has been developed. The simplest infectious disease model, which describes the most general mechanisms of immune protection, built on the assumption that the environment of the «organism» is homogeneous, in which all components of the process are instantly mixed by Marchuk is known. The infectious disease mathematical model by Marchuk for generalization of diffusion perturbations and various concentrated influences is generalized. The corresponding singularly perturbed model problem with delay is reduced to a sequence of problems without delay, for which the corresponding asymptotic developments of solutions are obtained. The results of numerical experiments, which illustrate the influence of spatially distributed diffusion «redistributions» on the nature of the viral disease in the presence of concentrated sources of antigens and donor antibodies are presented. A model decrease in the maximum level of antigens in the infection epicenter due to their diffusion «erosion» in the process of infectious disease development has been demonstrated. It is emphasized that even if the initial concentration or intensity of the pulsed viral source in a certain part of the infection will exceed some critical value (immunological barrier) due to diffusion «redistribution» for a short period of time, the supercritical concentration of viral agents may decrease to lower than the critical level and further neutralization of antigens can be provided by the available level of antibodies and a more economical procedure of injection solution with donor antibodies. That is, within this model, the «severity» of the viral disease in such cases can be reduced more rationally, at lower cost.