Impact of a cost functional on the optimal control and the cost-effectiveness: control of a spreading infection as a case study

Abstract

In applications of the optimal control theory to problems in medicine and biology, the dependency of the objective functional on the control itself is often a matter of controversy. In this paper, we explore the impact of the dependency using reasonably simple SIR and SEIRS epidemic models. To qualitatively compare the outcomes for different objective functionals, we apply the cost-effectiveness analysis. Our result shows that, at least for the comparatively inexpensive controls, the variation of the power at the controls in a biologically feasible range does not significantly affect the forms of the optimal controls and the corresponding optimal state solutions. Moreover, the costs and effectiveness are affected even less. At the same time, the dependency of the cost on the state variables can be very significant.

Investigation of singular regimens in a controlled model of psoriasis treatment

“…This cost depends not only on the price χ of the used inhibitor u 1 (t) and the price ν of the applied therapy u 2 (t), but also from the corresponding populations of T h 1 -cells and activated NK-cells exposed to them. In more detail, such terms in the objective functions are discussed in [3,13]. Note also that in the papers [18,19] the general cost of such biological treatment is determined in a different way, namely the integral part of the type:…”