Related papers: Optimal Control and Sensitivity Analysis of a Frac…
A Caputo-type fractional-order mathematical model for "metapopulation cholera transmission" was recently proposed in [Chaos Solitons Fractals 117 (2018), 37--49]. A sensitivity analysis of that model is done here to show the accuracy…
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…
We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of…
We propose a Caputo type fractional-order mathematical model for the transmission dynamics of tuberculosis (TB). Uniform asymptotic stability of the unique endemic equilibrium of the fractional-order TB model is proved, for any $\alpha \in…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
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…
We propose and study an optimal control model for malaria infection described by system of fractional differential equations. The model is formulated in terms of the left and right Caputo fractional derivatives. We determine the necessary…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
We propose and analyse an optimal control problem where the control system is a mathematical model for tuberculosis that considers reinfection. The control functions represent the fraction of early latent and persistent latent individuals…
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 consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be…
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. Numerical simulations are given using data from…
Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open-ended and challenging, a number of problems with fractional…
Tuberculosis remains a significant global health challenge, with millions of new cases reported annually. Recent studies suggest that expanding the accessibility of TB intervention programs can lead to a substantial decrease in both TB…
A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in…
Distributed-order fractional non-local operators have been introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted…
Modeling human operator's dynamic plays a very important role in the manual closed-loop control system, and it is an active research area for several decades. Based on the characteristics of human brain and behaviour, a new kind of…
The main aim of the present work is to study and analyze a reaction-diffusion fractional version of the SIR epidemic mathematical model by means of the non-local and non-singular ABC fractional derivative operator with complete memory…
We review recent results obtained to solve fractional order optimal control problems with free terminal time and a dynamic constraint involving integer and fractional order derivatives. Some particular cases are studied in detail. A…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…