scholarly journals Optimal Control and Cost-Effectiveness Analysis of HIV Model with Educational Campaigns and Therapy

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 123-138
Author(s):  
. Marsudi ◽  
Noor Hidayat ◽  
Ratno Bagus Edy Wibowo
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Cost Effectiveness Analysis ◽  
Control Measures ◽  
Hiv Model ◽  
Effectiveness Analysis ◽  
Educational Campaigns

In this paper, we present a deterministic model for the transmission dynamics of HIV, in which educational campaigns and therapy are both important for disease management. We propose and analyze an optimal control problem to investigate the effectiveness and cost-effectiveness of three control measures (educational campaigns, therapy on infected individuals in the asymptomatic stage, and therapy on infected individuals in the pre-AIDS class). We formulate the appropriate optimal control problem and investigate the necessary conditions for disease control in order to determine the role of asymptomatic infection, pre-AIDS, and full-blown AIDS in the spread of HIV. Pontryagin’s Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. The fourth-order Runge-Kutta forward-backwards sweep numerical approximation method was used to solve the optimal control system. The Incremental Cost-Effectiveness Ratio (ICER) was calculated to investigate the cost-effectiveness of all possible combinations of the three control measures. Using cost-effectiveness analysis, we showed that control of therapy on pre-AIDS and a combination of control of educational campaigns and therapy on pre-AIDS provides the most cost-effective strategy to control the disease.

scholarly journals Optimal Control Problem for Cholera Disease and Cost-Effectiveness Analysis

2021 ◽  
Vol 53 (2) ◽  
pp. 200-2017
Author(s):  
Jhoana Patricia Romero-Leiton ◽  
Muhammad Ozair ◽  
Takasar Hussaing
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Cost Effectiveness Analysis ◽  
Effectiveness Analysis ◽  
Using Data ◽  
Theoretical Results

Cholera is a disease that continues to be a threat to public health globally and is an indicator of inequity and lack of social development in countries. For this reason, strategies for its control need to be investigated. In this work, an optimal control problem related to cholera disease was formulated by introducing personal protection, drug treatment and water sanitation as control strategies. First, the existence and characterization of controls to minimize the performance index or cost function was proved by using classic control theory. Then, the theoretical results were validated with numerical experiments by using data reported in the literature. Finally, the effectiveness and efficiency of the proposed controls were determined through a cost-effectiveness analysis. The results showed that the use of the three controls simultaneously is the cheapest and most effective strategy to control the disease.

scholarly journals Cost-Effectiveness Analysis of Optimal Control Measures for Tuberculosis

2014 ◽  
Vol 76 (10) ◽  
pp. 2627-2645 ◽  
Author(s):  
Paula Rodrigues ◽  
Cristiana J. Silva ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Cost Effectiveness Analysis ◽  
Control Measures ◽  
Effectiveness Analysis

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

Optimal Campaign Strategies in Fractional-Order Smoking Dynamics

2014 ◽  
Vol 69 (5-6) ◽  
pp. 225-231 ◽  
Author(s):  
Anwar Zeb ◽  
Gul Zaman ◽  
Il Hyo Jung ◽  
Madad Khan
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Necessary Conditions ◽  
Order Model ◽  
Campaign Strategies ◽  
Education Campaign ◽  
Fractional Order Model

This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin’s maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (2) ◽  
pp. 302-309 ◽  
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

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