An application of forward-backward difference approximation method on the optimal control problem in the transmission of tuberculosis model

2017 ◽  
Author(s):  
Z. Rahmah ◽  
B. Subartini ◽  
E. Djauhari ◽  
N. Anggriani ◽  
A. K. Supriatna
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Approximation Method ◽  
Difference Approximation ◽  
Tuberculosis Model

scholarly journals Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays

2021 ◽  
Vol 11 (1) ◽  
pp. 75-91
Author(s):  
Mohamed Elhia ◽  
Omar Balatif ◽  
Lahoucine Boujallal ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Delays ◽  
Control Strategies ◽  
Multiple Time ◽  
Optimal Controls ◽  
Loss To Follow Up ◽  
Tuberculosis Model

In this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extension of the classical SEIR model by dividing infectious patients in the compartment (I) into three categories: undiagnosed infected (I), diagnosed patients who are under treatment (T) and diagnosed patients who are lost to follow-up (L). We incorporate in our model delays representing the incubation period and the time needed for treatment. We also introduce three control variables in our delayed system which represent prevention, detection and the efforts that prevent the failure of treatment. The purpose of our control strategies is to minimize the number of infected individuals and the cost of intervention. The existence of the optimal controls is investigated, and a characterization of the three controls is given using the Pontryagin's maximum principle with delays. To solve numerically the optimality system with delays, we present an adapted iterative method based on the iterative Forward-Backward Sweep Method (FBSM). Numerical simulations performed using Matlab are also provided. They indicate that the prevention control is the most effective one. To the best of our knowledge, it is the first work to apply optimal control theory to a TB model which considers infectious patients diagnosis, loss to follow-up phenomenon and multiple time delays.

scholarly journals PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Wichai Witayakiattilerd
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Approximation Method ◽  
Pid Controller ◽  
Impulsive Differential Equations ◽  
Integral Form ◽  
Impulsive System ◽  
Slow Variable ◽  
Fast Variable

We study singular perturbation of impulsive system with a proportional-integral-derivative controller (PID controller) and solve an optimal control problem. The perturbation system comprises two important variables, a fast variable and a slow variable. Because of the complexity of the system, it is difficult to find its exact solution. This paper presents an approximation method for solving it. The aim of the approximation method is to reduce the complexity of the system by eliminating the fast variable. The solution of the method is expressed in an integral form, and it is called an approximated mild solution of the perturbed system. An example is provided to illustrate our result.

scholarly journals Numerical Methods for Solving Optimal Control Problem Using Scaling Boubaker Function

2020 ◽  
Vol 25 (2) ◽  
pp. 78-89 ◽  
Author(s):  
Eman Hassan Ouda Alfrdji ◽  
Imad Noah Ahmed
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Approximation Method ◽  
Numerical Examples ◽  
Control Parameterization ◽  
Matlab Program ◽  
And Control

      In this paper, the approximation method was used for solving optimal control problem (OCP), two techniques for state parameterization and control parameterization have been considered with the aid of Scaling Polynomials (SBP) represent a new important technique for solving (OCP’s). The algorithms were illustrated by several numerical examples using Matlab program. The results were evaluated and graphed to show the accuracy  of the methods.

Sign in / Sign up

Export Citation Format

Share Document