Related papers: Stability and Optimal Control of a Delayed HIV Mod…
We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
In this study, we present a new epidemiological model, with contamination from confirmed and unreported. We also compute equilibria and study their stability without intervention strategies. Optimal control theory has proven to be a…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
In this paper, we study the stability of suboptimal H-infinity controllers for time-delay systems. The optimal H-infinity controller may have finitely or infinitely many unstable poles. A stable suboptimal H-infinity controller design…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
The search to understand how the HIV virus spreads inside the human body and how the immune response works to control it has motivated studies related to Mathematical Immunology. Actually, researches include the idea of mathematical models…
Human immunodeficiency virus (HIV-1 or simply HIV) induces a persistent infection, which in the absence of treatment leads to AIDS and death in almost all infected individuals. HIV infection elicits a vigorous immune response starting about…
Existing strategies for determining the optimal treatment or monitoring strategy typically assume unlimited access to resources. However, when a health system has resource constraints, such as limited funds, access to medication, or…
We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure…
We construct a seven-component model of the in-host dynamics of the Human Immunodeficiency Virus Type-1 (i.e, HIV) that accounts for latent infection and the propensity of viral mutation. A dynamical analysis is conducted and a theorem is…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
Recent clinical studies have shown that HIV disease pathogenesis can depend strongly on many factors at the time of transmission, including the strength of the initial viral load and the local availability of CD4+ T-cells. In this article,…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
We investigate the time-optimal control problem in SIR (Susceptible-Infected-Recovered) epidemic models, focusing on different control policies: vaccination, isolation, culling, and reduction of transmission. Applying the Pontryagin's…
In this paper we consider the evolution of the HIV infection under a highly effective treatment based on a combination of RTI and/or PI drugs. This is usually modelled with a set of ODEs where the drug efficacy is a constant. In this paper…
This paper investigates stable suboptimal H-infinity controllers for a class of single-input single-output time-delay systems. For a given plant and weighting functions, the optimal controller minimizing the mixed sensitivity (and the…
We consider an optimal control problem with tracking-type cost functional constrained by the Cattaneo equation, which is a well-known model for delayed heat transfer. In particular, we are interested the asymptotic behaviour of the optimal…
We consider the basic model of virus dynamics in the modeling of Human Immunodeficiency Virus (HIV), in a 2D heterogenous environment. It consists of two ODEs for the non-infected and infected $CD_4^+$ $T$ lymphocytes, $T$ and $I$, and a…
Chronic infections of the human immunodeficiency virus (HIV) create a very complex co-evolutionary process, where the virus tries to escape the continuously adapting host immune system. Quantitative details of this process are largely…