Marchuk's models of infection diseases: new developments

TL;DR

This paper discusses advancements in Marchuk's mathematical models of infectious diseases, incorporating distributed control to better represent antibody concentration dynamics through delay differential equations.

Contribution

It introduces a novel distributed control mechanism into Marchuk's existing models, enhancing their realism and applicability in immunology modeling.

Findings

Distributed control improves model accuracy.

Antibody dynamics are better captured with the new approach.

Models can now incorporate average antibody concentration changes.

Abstract

We consider mathematical models of infection diseases built by G.I. Marchuk in his well known book on immunology. These models are in the form of systems of ordinary delay differential equations. We add a distributed control in one of the equations describing the dynamics of the antibody concentration rate. Distributed control looks here naturally since the change of this concentration rather depends on the corresponding average value of the difference of the current and normal antibody concentrations on the time interval than on their difference at the point t only.