Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model
In this paper, we aim to investigate optimal control to a new mathematical model that describes agree-disagree opinions during polls, which we presented and analyzed in Bidah et al., 2020. We first present the model and recall its different compartments. We formulate the optimal control problem by s...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/5864238 |
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| _version_ | 1832561155054239744 |
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| author | Sara Bidah Omar Zakary Mostafa Rachik |
| author_facet | Sara Bidah Omar Zakary Mostafa Rachik |
| author_sort | Sara Bidah |
| collection | DOAJ |
| description | In this paper, we aim to investigate optimal control to a new mathematical model that describes agree-disagree opinions during polls, which we presented and analyzed in Bidah et al., 2020. We first present the model and recall its different compartments. We formulate the optimal control problem by supplementing our model with a objective functional. Optimal control strategies are proposed to reduce the number of disagreeing people and the cost of interventions. We prove the existence of solutions to the control problem, we employ Pontryagin’s maximum principle to find the necessary conditions for the existence of the optimal controls, and Runge–Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system, and we perform numerical simulations using various initial conditions and parameters to investigate several scenarios. Finally, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling to study the influence of various parameters on the objective functional and to identify the most influential parameters. |
| format | Article |
| id | doaj-art-7eaba6a2f930463db152bf71ad99d41b |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-7eaba6a2f930463db152bf71ad99d41b2025-02-03T01:25:45ZengWileyInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/58642385864238Modeling and Control of the Public Opinion: An Agree-Disagree Opinion ModelSara Bidah0Omar Zakary1Mostafa Rachik2Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoIn this paper, we aim to investigate optimal control to a new mathematical model that describes agree-disagree opinions during polls, which we presented and analyzed in Bidah et al., 2020. We first present the model and recall its different compartments. We formulate the optimal control problem by supplementing our model with a objective functional. Optimal control strategies are proposed to reduce the number of disagreeing people and the cost of interventions. We prove the existence of solutions to the control problem, we employ Pontryagin’s maximum principle to find the necessary conditions for the existence of the optimal controls, and Runge–Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system, and we perform numerical simulations using various initial conditions and parameters to investigate several scenarios. Finally, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling to study the influence of various parameters on the objective functional and to identify the most influential parameters.http://dx.doi.org/10.1155/2020/5864238 |
| spellingShingle | Sara Bidah Omar Zakary Mostafa Rachik Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model International Journal of Differential Equations |
| title | Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model |
| title_full | Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model |
| title_fullStr | Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model |
| title_full_unstemmed | Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model |
| title_short | Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model |
| title_sort | modeling and control of the public opinion an agree disagree opinion model |
| url | http://dx.doi.org/10.1155/2020/5864238 |
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