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.

scholarly journals A Spatiotemporal Prey-Predator Discrete Model and Optimal Controls for Environmental Sustainability in the Multifishing Areas of Morocco

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Amine El Bhih ◽  
Youssef Benfatah ◽  
Soukaina Ben Rhila ◽  
Mostafa Rachik ◽  
Adil El Alami Laaroussi
Keyword(s):  
Environmental Sustainability ◽  
Control Strategies ◽  
Discrete Version ◽  
Optimal Controls ◽  
Time Model ◽  
Top Predators ◽  
Realistic Description ◽  
Theoretical Results ◽  
Forward Backward Sweep Method

In this work, we propose a multifishing area prey-predator discrete-time model which describes the interaction between the prey and middle and top predators in various areas, which are connected by their movements to their neighbors, to provide realistic description prey effects of two predators. A grid of colored cells is presented to illustrate the entire domain; each cell may represent a subdomain or area. Next, we propose two harvesting control strategies that focus on maximizing the biomass of prey, in the targeted area, and minimizing the biomass of middle and top predators coming from the neighborhood of this targeted area to ensure sustainability and maintain a differential chain system. 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.

scholarly journals Modeling a Rumor Propagation in Online Social Network: An Optimal Control Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Rachid Ghazzali ◽  
Amine El Bhih ◽  
Adil El Alami Laaroussi ◽  
Mostafa Rachik
Keyword(s):  
Social Networks ◽  
Optimal Control ◽  
Control Strategy ◽  
Online Social Network ◽  
Optimal Controls ◽  
Control Approach ◽  
The Maximum Principle ◽  
Rumor Propagation ◽  
Optimal Control Approach

We propose to model the phenomenon of the spread of a rumor in social networks in this paper. From an existing SIR model, we manipulate a new one that is based on the model of cholera in order to take into account professional pages that specialize in spreading rumors. In the second part, we introduce a control strategy to fight against the diffusion of the rumor. Our main objective is to characterize the three optimal controls that minimize the number of spreader users, fake pages, and the corresponding costs. For that matter, using the maximum principle of Pontryagin, we prove the existence and we give characterization of our controls. Numerical simulations are given to concretize our approach.

scholarly journals On Characterization of Optimal Control Model of Whooping Cough

2021 ◽  
pp. 175-188
Author(s):  
A. S. Ismail ◽  
Y. O. Aderinto
Keyword(s):  
Optimal Control ◽  
Whooping Cough ◽  
Equilibrium Points ◽  
Public Health Problem ◽  
Sweep Method ◽  
Optimal Control Strategy ◽  
Runge Kutta Method ◽  
Disease Free ◽  
Forward Backward Sweep Method

Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.

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 Strategy for a Discrete Time Smoking Model with Specific Saturated Incidence Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Abderrahim Labzai ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Discrete Time ◽  
Control Strategy ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Heavy Smokers

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy.

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.

Near-optimal control problems for forward-backward regime-switching systems

2020 ◽  
Vol 26 ◽  
pp. 94
Author(s):  
Min Li ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Regime Switching ◽  
Hamiltonian Function ◽  
Minimum Condition ◽  
Optimal Controls ◽  
Diffusion Term ◽  
Finite State ◽  
Forward Diffusion ◽  
Theoretical Results ◽  
Near Optimality

This paper investigates the near-optimality for a class of forward-backward stochastic differential equations (FBSDEs) with continuous-time finite state Markov chains. The control domains are not necessarily convex and the control variables do not enter forward diffusion term. Some new estimates for state and adjoint processes arise naturally when we consider the near-optimal control problem in the framework of regime-switching. Inspired by Ekeland’s variational principle and a spike variational technique, the necessary conditions are derived, which imply the near-minimum condition of the Hamiltonian function in an integral sense. Meanwhile, some certain convexity conditions and the near-minimum condition are sufficient for the near-optimal controls with order ε1/2. A recursive utility investment consumption problem is discussed to illustrate the effectiveness of our theoretical results.

scholarly journals CHOICE OF THE OPTIMAL CONTROL STRATEGY FOR THE DUPLEX-PROCESS OF INDUCTION MELTING OF CONSTRUCTIONAL IRON

2018 ◽  
Vol 4 ◽  
pp. 3-13 ◽  
Author(s):  
Iegor Dymko
Keyword(s):  
Optimal Control ◽  
Thermal Treatment ◽  
Control Strategy ◽  
Control Object ◽  
Effective Control ◽  
Induction Melting ◽  
Optimal Controls ◽  
Optimal Control Strategy ◽  
Final State ◽  
Duplex Process

To find effective control of the duplex process of induction melting in conditions of uncertainties, a method was suggested that made it possible to obtain optimal controls for both stages: melting and thermal treatment. It is shown how the search for an optimal melting control strategy can be performed using the theory of statistical games. At the same time, it is selected which of the melting regimes will be the best with the existing provision of the shop with charge materials. The costs of melting are the total costs, consisting of: – costs for the selected technological mode of melting (including costs for materials), – costs from the potential rejection of castings due to the non-conformity of the chemical composition of the alloy to the specified – due to the incorrectly chosen melting mode, – costs from the downtime due to the fact that the necessary amount of metal from the furnace is not delivered to the conveyor. The choice of an optimal control strategy in accordance with the proposed procedure can remove uncertainty in the evaluation of input process variables if they are taken as indicators of the charge quality. To find the optimal control at the stage of the heat treatment, a multialternative description of the final state is proposed on the basis of solving the problem of ridge analysis. This makes it possible to remove the uncertainty in the estimation of the final state, which allows a lot of optimal solutions in the sense of achieving a given quality. It is shown that such approach makes it possible not only to synthesize the optimal controller of the temperature regime on the basis of an analysis of the system of differential equations describing the control object, but also the application of the Pontryagin maximum principle to search for optimal control of the thermal treatment. The proposed method allows to determine the optimal control in the sense of stabilization for a given process parameter of the duplex process of induction melting. The resulting solutions form the necessary logical conditions for the logic control unit for the control system of the duplex induction melting process.

scholarly journals Defending against Online Social Network Rumors through Optimal Control Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Da-Wen Huang ◽  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Yuan Yan Tang ◽  
Jichao Bi
Keyword(s):  
Social Networks ◽  
Optimal Control ◽  
Online Social Networks ◽  
Online Social Network ◽  
Computer Experiments ◽  
Cost Effective ◽  
Rumor Spreading ◽  
Control Approach ◽  
The Cost ◽  
Optimal Control Approach

Rumors have been widely spread in online social networks and they become a major concern in modern society. This paper is devoted to the design of a cost-effective rumor-containing scheme in online social networks through an optimal control approach. First, a new individual-based rumor spreading model is proposed, and the model considers the influence of the external environment on rumor spreading for the first time. Second, the cost-effectiveness is recommended to balance the loss caused by rumors against the cost of a rumor-containing scheme. On this basis, we reduce the original problem to an optimal control model. Next, we prove that this model is solvable, and we present the optimality system for the model. Finally, we show that the resulting rumor-containing scheme is cost-effective through extensive computer experiments.

scholarly journals Mathematical Modeling and Optimal Control Strategy for a Discrete Time Drug Consumption Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Abderrahim Labzai ◽  
Abdelfatah Kouidere ◽  
Bouchaib Khajji ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Control Strategy ◽  
Drug Users ◽  
Control Strategies ◽  
Drug Consumption ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Discrete Mathematical Model

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of drug consumption. The population that we are going to study is divided into six compartments: potential drug users, light drug users, heavy drug users, heavy drug users-dealers and providers, temporary quitters of drug consumption, and permanent quitters of drug consumption. Our objective is to find the best strategy to reduce the number of light drug users, heavy drug users, heavy drug users-dealers and providers, and temporary quitters of drug consumption. We use four control strategies which are awareness programs through media and education, preventing contact through security campaigns, treatment, and psychological support along with follow-up. Pontryagin’s maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the effectiveness of the optimization strategy.

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