Distributed control in stabilization of a model of infection diseases

In this paper, we consider a model of infection diseases built by G.I. Marchuk in the form of system of ordinary differential equations. A distributed feedback control is added to achieve a stabilization in the neighborhood of a suitable stationary solution in the case where other methods do not work. An idea of a reduction of integro-differential systems to ones of ordinary differential equations is proposed. We study the exponential stability of a stationary point of the integrodifferential system.