scholarly journals Fast iterative solver for the optimal control of time‐dependent PDEs with Crank–Nicolson discretization in time

2021 ◽  
Author(s):  
Santolo Leveque ◽  
John W. Pearson
Keyword(s):  
Optimal Control ◽  
Time Dependent ◽  
Iterative Solver ◽  
Crank Nicolson

Estimating the impact of antiretroviral therapy on HIV-TB co-infection: Optimal strategy prediction

2020 ◽  
pp. 2150004
Author(s):  
Tanvi ◽  
Rajiv Aggarwal
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Treatment Strategies ◽  
Hiv Treatment ◽  
Time Dependent ◽  
Control Parameters ◽  
Treatment Rate ◽  
Tb Treatment ◽  
The Cost ◽  
The Impact

In this paper, a nonlinear population model for HIV-TB co-infection has been proposed. The model is incorporated with the effect of early and late initiation of HIV treatment in co-infectives already on TB treatment, on the occurrence of Immune Reconstitution Inflammatory syndrome (IRIS). A 15-dimensional (15D) mathematical model has been developed in this study. We begin with considering constant treatment rates and thereafter, proceed to time-dependent treatment rates for co-infectives as control parameters. The basic reproduction number, a threshold quantity, corresponding to each HIV and TB sub-model has been computed in case of constant controls. With constant values of control parameters, mathematical analysis shows the existence and local stability of the disease-free equilibrium point and the endemic equilibrium point for the model. Together with time-dependent parameters, an optimal control problem is introduced and solved using Pontryagin’s maximum principle with an objective to minimize the number of infectives and disease induced deaths along with the cost of treatment. Numerical simulations are performed to examine the effect of reproduction numbers on control profiles and to identify, the ideal combination of treatment strategies which provides minimum burden on a society. Numerical results imply that if both HIV and TB are endemic in the population, then in order to bring in minimum burden from the co-infection, optimal control efforts must be enforced rather than constant treatment rate.

scholarly journals Deterministic Epidemic Models for Ebola Infection with Time-Dependent Controls

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Eric Okyere ◽  
Johnson De-Graft Ankamah ◽  
Anthony Kodzo Hunkpe ◽  
Dorcas Mensah
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Ebola Virus ◽  
Virus Disease ◽  
Control Strategies ◽  
Hamiltonian Function ◽  
Epidemic Models ◽  
Adjoint Equations ◽  
Time Dependent ◽  
Control Analysis

In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment, and educational campaign as time-dependent control functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and Pontryagin’s maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with the fourth-order Runge–Kutta method is used to solve the optimality system for the various control strategies. From our numerical illustrations, we can conclude that effective educational campaigns and vaccination of susceptible individuals as well as effective treatments of infected individuals can help reduce the disease transmission.

scholarly journals Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 3-6 ◽  
Author(s):  
John W. Pearson ◽  
Martin Stoll ◽  
Andrew J. Wathen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Time Dependent ◽  
Control Problems
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