Related papers: Immune Therapeutic Strategies Using Optimal Contro…
In this article, a well-known mathematical model of cancer immunotherapy is discussed and used to represent therapeutic protocols for cancer treatment. The optimal control problem is formulated based on the Pontryagin maximum principle to…
Optimal control theory in epidemiology has been used to establish the most effective intervention strategies for managing and mitigating the spread of infectious diseases while considering constraints and costs. Using Pontryagin's Maximum…
Mathematical modelling can help to explain the nature and dynamics of infection transmissions, as well as support a policy for implementing those strategies that are most likely to bring public health and economic benefits. The paper…
The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics. The main feature of our study is the presence of state constraints (related to intensive care units ICU capacity) and…
In this paper we consider an optimal control problem arising from a chemotherapeutic drug treatment for tumor cells in a living tissue. The mathematical model for the interaction of chemotherapeutic drug and the normal, tumor and immune…
We review the optimal control of systems modeling the dynamics of tuberculosis. Time dependent control functions are introduced in the mathematical models, representing strategies for the improvement of the treatment and cure of active…
While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health…
Cell heterogeneity plays an important role in patient responses to drug treatments. In many cancers, it is associated with poor treatment outcomes. Many modern drug combination therapies aim to exploit cell heterogeneity, but determining…
Control of an inflammatory immune response is still an ongoing research. Here, a strategy consisting of manipulating a pro and anti-inflammatory mediator is considered. Already existing and promising model-based techniques suffer…
Simple ideas, endowed from the mathematical theory of control, are used in order to analyze in general grounds the human immune system. The general principles are minimization of the pathogen load and economy of resources. They should…
The relationship between epidemiology, mathematical modeling and computational tools allows to build and test theories on the development and battling of a disease. This PhD thesis is motivated by the study of epidemiological models applied…
An optimal control problem for a model of tumor growth is studied. In a given subdomain, it is required to minimize the density of tumor cells, while the drug concentration in tissue is limited by given minimal and maximal values. Based on…
We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected…
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…
This paper investigates the optimal control of an epidemic governed by a SEIR model with an operational delay in vaccination. We address the mathematical challenge of imposing hard healthcare capacity constraints (e.g., ICU limits) over an…
We present and compare two different optimal control approaches applied to SEIR models in epidemiology, which allow us to obtain some policies for controlling the spread of an epidemic. The first approach uses Dynamic Programming to…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
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…
This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of…
In this paper, we study the optimal control for an SEIR model adapted to the vaccination strategy of susceptible individuals. There are factors associated with a vaccination campaign that make this strategy not only a public health issue…