ABSTRACT
Anthrax is a fatal infectious disease which can affect animals and humans alike. Anthrax outbreaks occur periodically in animals, and they are of particular concern in herbivores, due to substantial economic consequences associated with animal death. The purpose of this study is to develop optimal control interventions that focus on vaccinating susceptible animals and/or removing infected carcasses. Our mathematical goal is to minimize the infectious animal population while reducing the cost of interventions. Optimal control interventions are derived theoretically, and numerical results with conclusions are presented.
Subject(s)
Anthrax/veterinary , Models, Biological , Animals , Anthrax/prevention & control , Anthrax/transmission , Anthrax Vaccines/therapeutic use , Computer Simulation , Disease Outbreaks/prevention & control , Disease Outbreaks/veterinary , Herbivory , Humans , Mathematical Concepts , Vaccination/veterinaryABSTRACT
HIV infection is one of the most difficult infections to control and manage. The most recent recommendations to control this infection vary according to the guidelines used (US, European, WHO) and are not patient-specific. Unfortunately, no two individuals respond to infection and treatment quite the same way. The purpose of this paper is to make use of the uncertainty and sensitivity analysis to investigate possible short-term treatment options that are patient-specific. We are able to identify the most significant parameters that are responsible for ART outcome and to formulate some insights into the ART success.
Subject(s)
Anti-HIV Agents/administration & dosage , HIV Infections/drug therapy , Models, Biological , CD4-Positive T-Lymphocytes/virology , Computer Simulation , Drug Administration Schedule , HIV Infections/virology , Humans , Mathematical Concepts , Treatment Outcome , UncertaintyABSTRACT
The main goal of this study was to develop a theoretical short- and long-term optimal control treatment of HIV infection of [Formula: see text] cells. The aim of the mathematical model used herein is to make the free HIV virus particles in the blood decrease, while administering a treatment that is less toxic to patients. Pontryagin's classical control theory is applied to a mathematical model of HIV infection of [Formula: see text] cells characterized by a system of nonlinear differential equations with the following unknown functions: the concentration of susceptible [Formula: see text] cells, [Formula: see text] cells infected by the HIV viruses and free HIV virus particles in the blood.