scholarly journals Existence and characterization of optimal control in mathematics model of diabetics population

2018 ◽  
Vol 983 ◽  
pp. 012069 ◽  
Author(s):  
A H Permatasari ◽  
R H Tjahjana ◽  
T Udjiani
Keyword(s):  
Optimal Control ◽  
Mathematics Model

scholarly journals Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Mostafa Tahiri ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Optimality Conditions ◽  
Fractional Derivatives ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Derivative Operator ◽  
Sir Epidemic ◽  
Non Local

<p style='text-indent:20px;'>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 effects. Existence and uniqueness of solution for the proposed fractional model is proved. Existence of an optimal control is also established. Then, necessary optimality conditions are derived. As a consequence, a characterization of the optimal control is given. Lastly, numerical results are given with the aim to show the effectiveness of the proposed control strategy, which provides significant results using the AB fractional derivative operator in the Caputo sense, comparing it with the classical integer one. The results show the importance of choosing very well the fractional characterization of the order of the operators.</p>

scholarly journals A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Amine El Bhih ◽  
Rachid Ghazzali ◽  
Soukaina Ben Rhila ◽  
Mostafa Rachik ◽  
Adil El Alami Laaroussi
Keyword(s):  
Optimal Control ◽  
Online Social Network ◽  
Discrete Version ◽  
Optimal Controls ◽  
Optimal Control Strategy ◽  
Rumor Spreading ◽  
Rumor Propagation ◽  
Theoretical Results ◽  
Forward Backward Sweep Method

In this paper, a new rumor spreading model in social networks has been investigated. We propose a new version primarily based on the cholera model in order to take into account the expert pages specialized in the dissemination of rumors from an existing IRCSS model. In the second part, we recommend an optimal control strategy to fight against the spread of the rumor, and the study aims at characterizing the three optimal controls which minimize the number of spreader users, fake pages, and corresponding costs; theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

OPTIMAL CONTROL FOR A NONLINEAR n-DIMENSIONAL COMPETING SYSTEM WITH AGE-STRUCTURE

2012 ◽  
Vol 05 (03) ◽  
pp. 1260008 ◽  
Author(s):  
ZHI-XUE LUO ◽  
JIAN-YU YANG ◽  
YA-JUAN LUO
Keyword(s):  
Optimal Control ◽  
Age Structure ◽  
Normal Cone ◽  
Equation System ◽  
Optimal Harvesting ◽  
Order Partial Differential Equation ◽  
Differential Equation System ◽  
Optimal Control Strategy ◽  
First Order

This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland's variational principle, the existence and unique characterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.

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.

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