DECISION-MAKING WHEN PREDICTING THE DYNAMICS OF A VIRAL INFECTION TAKING INTO ACCOUNT THE DIFFUSION-CONVECTION MIGRATION OF ACTIVE FACTORS BY SEVERAL WAYS IN THE CONDITIONS OF IMMUNOTHERAPY

Abstract

Based on the problem of distinguishing different conditions for the spread of antigens, antibodies, and medicinal substances in the intercellular space and the lymphatic system, when predicting the dynamics of a viral infection, a modification of the mathematical model of an infectious disease was carried out for to take into account the influence of various ways of migration of active factors in the body’s environment. The solution of the model singularly perturbed problem with a delay is obtained based on adapted computing technology, which provides a stepwise numerical asymptotic approximation of a specially constructed sequence of problems without delay as a perturbation of the solutions of the corresponding degenerate problems. The results of computer modeling illustrate the predictive contribution of several ways of migration of active factors to the process of infectious disease development. It is noted that the effectiveness of immunological drugs, among other things, will be influenced by the conditions determined by the migration of donor antibodies in the body’s environment, which must be taken into account in decision-making systems regarding the formation of appropriate rational disease treatment programs. Keywords: infectious disease model, dynamic systems with delay, heterodiffusion in two ways, asymptotic methods, singularly perturbed problems, concentrated influences.