Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs

Abstract

Abstract:The representation of the cost of a therapy is a key element in the formulation of the optimal control problem for the treatment of infectious diseases. The cost of the treatment is usually modeled by a function of the price and quantity of drugs administered; this function should be the cost as subjectively perceived by the decision-maker. Nevertheless, in literature, the choice of the cost function is often simply done to make the problem more tractable. A specific problem is also given by very expensive therapies in the presence of a very high number of patients to be treated. Firstly, we investigate the optimal treatment of infectious diseases in the simplest case of a two-class population (susceptible and infectious people) and compare the results coming from five different shapes of cost functions. Finally, a model for the treatment of the HCV virus using the blowing-up cost function is investigated. Some numerical simulations are also given.

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

“…[23][24][25][26][27] and references therein. The by far largest part of these works deals with optimal control of epidemics through vaccination and immunization [28][29][30][31], medical treatment [32,33] and combinations thereof [34][35][36][37][38][39]. Significantly fewer papers are concerned with the optimal control of transmission dynamics and the mitigation of epidemics through social distancing measures.…”

The Continuous Classical Optimal Boundary Control of a Couple Linear Elliptic Partial Differential Equations

“…) and is a unknown constant, , with . By substituting (12) in (11), with ⃗ , to get: Easily one can get that through using assumption (A-a), problem (14) has a unique solution which gives the existence of a unique solution of (11).…”

“…The optimal control problems play an important role in many fields of real life problems, for examples in robotics [Braun & Vijayakumar 2013], in an electric power [Wang & Lin 2013], in civil engineering [Amini & Afshar 2008], in Aeronautics and Astronautics [Lessard & Lall 2012], in medicine [Liddo 2016], in economic [Derakhshan 2015], in heat conduction [Yilmaz & Mahariq 2016], in biology [Chalak 2014] and many others fields.…”

The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Elliptic Partial Differential Equations with State Constraints

“…The optimal control problems play an important role in many fields in the real life problems, for examples in robotics [1], in an electric power [2], in civil engineering [3], in Aeronautics and Astronautics [4], in medicine [5], in economic [6], in heat conduction [7], in biology [8] and many others fields. This importance of optimal control problems encouraged many researchers interested to study the optimal control problems of systems are governed either by nonlinear ordinary differential equations as in [9] and [10] or by linear partial differential equations as in [11] or are governed by nonlinear partial differential equations either of a hyperbolic type as in [12] or of a parabolic type as in [13] or by an elliptic type as in [14], or optimal control problem are governed either by a couple of nonlinear partial differential equations of a hyperbolic type as in [15] or of a parabolic type as in [16] or by an elliptic type as in [17], or of an elliptic type but involve a boundary control as in [18].…”