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Optimal Control Problem for an Electoral Behavior Model

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Abstract

In this paper, we propose a compartmental model where the electorate is divided into six classes or sub-populations: potential electors (P), unregistered individuals (U), registered individuals (R), temporary abstainers (\(\hbox {A}^t\)), voters for the political party (\(\hbox {V}^f\)) and voters against the political party (\(\hbox {V}^a\)). Our model describes the electoral behavior of citizens with regards to the electoral process in general and with regards to a political party in particular. It includes three controls representing strategies that can help to increase the participation rate at elections and boost a political party’s chances of getting more votes. We formulate an optimal control problem based on the proposed model. Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical results carried out using real data with the Moroccan legislative elections of 2016 show the performance of our optimization strategies.

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Authors and Affiliations

  1. Laboratory of Dynamical Systems, Mathematical Engineering Team, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco

    Omar Balatif

  2. MAEGE Laboratory, Faculty of Legal, Economic and Social Sciences, Hassan II University of Casablanca, Casablanca, Morocco

    Mohamed El Hia

  3. Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Casablanca, Morocco

    Mostafa Rachik

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  1. Omar Balatif
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  2. Mohamed El Hia
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  3. Mostafa Rachik
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Correspondence to Omar Balatif.

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Balatif, O., El Hia, M. & Rachik, M. Optimal Control Problem for an Electoral Behavior Model. Differ Equ Dyn Syst 31, 233–250 (2023). https://doi.org/10.1007/s12591-020-00533-9

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