scholarly journals Optimal control strategy for a HIV infection model via fourier series

2013 ◽  
Vol 9 (2) ◽  
pp. 87-94 ◽  
Keyword(s):  
Optimal Control ◽  
Fourier Series ◽  
Nonlinear System ◽  
Treatment Protocol ◽  
Infection Model ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Optimal Control Strategy ◽  
Hiv Infection Model ◽  
The Cost

Abstract This paper proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the uninfected CD4+T cells and minimize the cost of drug, utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus(HIV). The optimal pair of control and trajectories of this nonlinear system with quadratic cost functional is obtained by Fourier series approximation. The method is based upon expanding time varying functions in the nonlinear system as their Fourier series, using the operational matrices for integration and product. The problem is reduced into a set of algebraic equations

scholarly journals Optimal Control of a Delayed HIV Infection Model via Fourier Series

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Gh. Ghanbari ◽  
M. H. Farahi
Keyword(s):  
Optimal Control ◽  
Fourier Series ◽  
Delay System ◽  
Infection Model ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Immunodeficiency Virus ◽  
Fourier Series Approximation ◽  
Hiv Infection Model ◽  
Nonlinear Delay

We present a delayed optimal control which describes the interaction of the immune system with the human immunodeficiency virus (HIV) and CD4+ T-cells. In order to improve the therapies, treatment and the intracellular delays are incorporated into the model. The optimal control in this model represents the efficiency of drug treatment in preventing viral production and new infections. The optimal pair of control and trajectories of this nonlinear delay system with quadratic cost functional is obtained by Fourier series approximation. The method is based on expanding time varying functions in the nonlinear delay system into their Fourier series with unknown coefficients. Using operational matrices for integration, product, and delay, the problem is reduced to a set of nonlinear algebraic equations.

Parameters estimation of HIV infection model of CD4+T-cells by applying orthonormal Bernstein collocation method

2018 ◽  
Vol 11 (02) ◽  
pp. 1850020 ◽  
Author(s):  
Farshid Mirzaee ◽  
Nasrin Samadyar
Keyword(s):  
T Cells ◽  
Nonlinear System ◽  
Hiv Infection ◽  
Initial Conditions ◽  
Bernstein Polynomials ◽  
Nonlinear Ordinary Differential Equation ◽  
Parameters Estimation ◽  
Infection Model ◽  
Algebraic Equations ◽  
Hiv Infection Model

The HIV infection model of CD4[Formula: see text][Formula: see text]T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials (OBPs). By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton’s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.

scholarly journals The Optimal Control Strategy of Virus Transmission Based on Caputo-Fabrizio Order

2021 ◽  
Vol 9 ◽  
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xue Yang ◽  
Zhen Wang
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Virus Transmission ◽  
Real Data ◽  
Infection Model ◽  
Optimal Control Strategy ◽  
Optimal Therapy ◽  
Therapy Strategy ◽  
B Virus ◽  
The Cost

Hepatitis B virus (HBV) is a serious threat to human health as it can cause the chronic hepatitis B, and eventually liver cancer. It also has become one of the major threats to public health in the world. In this paper, considering the rationality of using standard incidence in Caputo-Fabrizio fractional order HBV infection model, we propose a model with standard incidence. The analysis of local stability about the equilibrium and the simulation of global stability are given. We also use the real data to estimate the parameters of this model. The simulation results can fit the data well. Moreover, we propose an optimal control model and give the optimal therapy strategy, which show that optimal therapy can reduce the cost and side effects while ensuring the therapeutic effect.

Numerical solution of time-delay optimal control problems by the operational matrix based on Hartley series

2021 ◽  
pp. 014233122110533
Author(s):  
Mahmood Dadkhah ◽  
Kamal Mamehrashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Main Idea ◽  
Control Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
The Cost ◽  
And Control

In this paper, a numerical technique based on the Hartley series for solving a class of time-delayed optimal control problems (TDOCPs) is introduced. The main idea is converting such TDOCPs into a system of algebraic equations. Thus, we first expand the state and control variables in terms of the Hartley series with undetermined coefficients. The delay terms in the problem under consideration are expanded in terms of the Hartley series. Applying the operational matrices of the Hartley series including integration, differentiation, dual, product, delay, and substituting the estimated functions into the cost function, the given TDOCP is reduced to a system of algebraic equations to be solved. The convergence of the proposed method is extensively investigated. At last, the precision and applicability of the proposed method is studied through different types of numerical examples.

scholarly journals Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li
Keyword(s):  
Optimal Control ◽  
Rapid Development ◽  
Hamiltonian Function ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Optimal Control Strategy ◽  
Epidemic Dynamics ◽  
Optimization Control ◽  
The Cost ◽  
The Pontryagin Maximum Principle

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

Shifted Boubaker Lagrangian approach for solving biological systems

2018 ◽  
Vol 11 (03) ◽  
pp. 1850039 ◽  
Author(s):  
Kourosh Parand ◽  
Hossein Yousefi ◽  
Mina Fotouhifar ◽  
Mehdi Delkhosh ◽  
Mehdi Hosseinzadeh
Keyword(s):  
Mathematical Models ◽  
Hantavirus Infection ◽  
Infection Model ◽  
Algebraic Equations ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Immunodeficiency Virus ◽  
Nonlinear Algebraic Equations ◽  
Newton Iteration Method ◽  
Hiv Infection Model

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus (HIV) infection model of CD4[Formula: see text]T cells and the susceptible–infected–removed (SIR) epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian (SBL) method. This method reduces the solution of such system to a system of linear or nonlinear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge–Kutta (RK4) method and with the solutions obtained by some other methods in the literature.

New operational matrices approach for optimal control based on modified Chebyshev polynomials

2021 ◽  
Vol 2 (2) ◽  
pp. 68-78
Author(s):  
Anam Alwan Salih ◽  
Suha SHIHAB
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Chebyshev Polynomials ◽  
Optimization Technique ◽  
Computational Method ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Quadratic Optimal Control ◽  
Chebyshev Orthogonal Polynomial

The purpose of this paper is to introduce interesting modified Chebyshev orthogonal polynomial. Then, their new operational matrices of derivative and integration or modified Chebyshev polynomials of the first kind are introduced with explicit formulas. A direct computational method for solving a special class of optimal control problem, named, the quadratic optimal control problem is proposed using the obtained operational matrices. More precisely, this method is based on a state parameterization scheme, which gives an accurate approximation of the exact solution by utilizing a small number of unknown coefficients with the aid of modified Chebyshev polynomials. In addition, the constraint is reduced to some algebraic equations and the original optimal control problem reduces to optimization technique, which can be solved easily, and the approximate value of the performance index is calculated. Moreover, special attention is presented to discuss the convergence analysis and an upper bound of the error for the presented approximate solution is derived. Finally, some important illustrative examples of obtained results are shown and proved that powerful method in a simple way to get an optimal control of the considered.

A numerical approach for solving fractional optimal control problems with mittag-leffler kernel

2021 ◽  
pp. 107754632110169
Author(s):  
Hossein Jafari ◽  
Roghayeh M Ganji ◽  
Khosro Sayevand ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Approximate Solution ◽  
Optimal Control Problems ◽  
Fractional Integration ◽  
Numerical Approach ◽  
Control Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana–Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.

scholarly journals A new optimal control technique for solution of HIV infection model

2021 ◽  
Vol 40 ◽  
pp. 1-7
Author(s):  
Malihe Najafi ◽  
Hadi Basirzadeh
Keyword(s):  
Optimal Control ◽  
Power Series ◽  
Hiv Infection ◽  
Numerical Solutions ◽  
Control Technique ◽  
Infection Model ◽  
Control Power ◽  
Hiv Infection Model ◽  
Power Series Technique ◽  
Series Technique

In this paper, by means of the optimal control technique and power series technique,we introduce a new method, namely, the optimal control power series technique, bywhich one can obtain numerical solutions of the HIV infection model of CD4+T cells.The obtained approximate solution has shown good agreement with the experimentalresults and previous simulations using other methods.https://search.hthereadinghub.com/?uc=20180302&ad=appfocus1&source=d-lp0-bb9&uid=0d8983d2-5a26-4ec4-bba5-84ea234d1896&i_id=ebooks_100.7&page=newtab&

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