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Problems of control for immunological models. (English) Zbl 1102.92035
Summary: The paper deals with the analysis of some of G. I. Marchuk’s [Mathematical models in immunology. (1983; Zbl 0556.92006)] and G. I. Marchuk and R.V. Petrov’s [Vychisl. Protsessy Sist. 3, 5–11 (1985; Zbl 0596.92006)] models of the immune response of organisms. The models are described by using systems of functional-differential equations. In addition to problems of stability, statements of control problems for a simple immunological model with temperature reaction of organisms is also presented in the paper. Besides, conditions of asymptotic stability as a whole for the Marchuk-Petrov model of immunophysiological reactions of defense and the properties of controllability and stabilization are analyzed as well.
MSC:
92C50Medical applications of mathematical biology
34K35Functional-differential equations connected with control problems
34K20Stability theory of functional-differential equations