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.