Modeling of discrete control of antiviral immune response in conditions of uncertainty

Abstract

In this paper is considered numerically solving a problem of discrete control with uncertainty of the immune response in infectious disease. The problem of discrete control is described by a nonlinear system of ordinary differential equations with a retarded argument. Control under conditions of uncertainty implies that the parameter values are unknown and parameter estimation is adjusted as new experimental values become available. In order to solve this problem, the algorithm that allows us to construct a control function and at the same time to identify parameters within mathematical model of the infectious disease is proposed. By means of the proposed algorithm, the treatment programs based on an immunotherapy are constructed and parameters of the mathematical model of antiviral immune response are identified. It is shown that immunotherapy allows us to effectively cure the acute form of a disease.