Modeling of Abstinence Behavior on the Electoral Lists with Awareness Campaigns and Argumentative Schemes

Lazarus Kalvein Beay; Hasan S. Panigoro; Emli Rahmi; Dian Savitri

doi:10.5614/cbms.2024.7.2.4

Authors

Lazarus Kalvein Beay Division of Applied Mathematics, Department of Mathematics, Universitas Pattimura, Ambon 97233, Indonesia
Hasan S. Panigoro Biomathematics Research Group, Department of Mathematics, Universitas Negeri Gorontalo, Bone Bolango 96554, Indonesia
Emli Rahmi Biomathematics Research Group, Department of Mathematics, Universitas Negeri Gorontalo, Bone Bolango 96554, Indonesia
Dian Savitri Department of Mathematics, Universitas Negeri Surabaya, Surabaya 60231, Indonesia

DOI:

https://doi.org/10.5614/cbms.2024.7.2.4

Keywords:

Model of abstinence behaviour, awareness campaigns, argumentative scheme, reproductive number, sensitivity analysis, stability

Abstract

The most reasonable way to promote individual abstinence and increase voter turnout is through campaign interventions and schemes. Our paper introduces a deterministic model that captures the dynamics of citizens exercising their right to vote and the detrimental effect of abstainers on potential voters. The existence, basic reproductive number (R0) and local stability of abstinence behavior equilibrium points are determined by certain necessary conditions. The global stability of the abstaining-free point and abstaining point is achieved through the use of suitable Lyapunov functions. In addition, a sensitivity analysis of R0 was also performed. Moreover, we offer an ideal plan for an awareness program that supports politicians and officials in enhancing the registration rate of citizens on electoral lists with a level of effort. Our investigation reveals that utilizing the combination of an awareness campaign and argumentation schemes as time-dependent interventions drastically reduces abstention rates and greatly increases voter participation. By raising the values of awareness and registration rates, we can observe a decline in the basic reproductive number (R0). Our analytical results are supported by numerical simulations.

References

Kellermann, K.L., Political inequality, political participation, and support for populist parties, Constitutional Political Economy, 33(4), pp. 461-482, 2022.

Roberts, B.J., Struwig, J., Gordon, S.L. and Davids, Y.D., The unconvinced vote: The nature and determinants of voting intentions and the changing character of South African electoral politics, In Reflections on the 2019 South African General Elections, Routledge, pp. 117-134, 2020.

Lari, I., Pukelsheim, F. and Ricca, F., Mathematical modeling of electoral systems: analysis, evaluation, optimization. In memory of Bruno Simeone (1945?2010), Annals of Operations Research, 215, pp. 1-14, 2014.

Balatif, O., El Hia, M. and Rachik, M., Optimal control problem for an electoral behavior model, Differential Equations and Dynamical Systems, 31(1), pp. 233-250, 2023.

Balatif, O., Khajji, B. and Rachik, M., Mathematical modeling, analysis, and optimal control of abstinence behavior of registration on the electoral lists, Discrete Dynamics in Nature and Society, 2020(1), pp. 1-12, 2020.

Liu, H., Erdogan, A., Lin, R. and Tsao, H.S.J., Mathematical models of political districting for more representative governments, Computers & Industrial Engineering, 140, pp. 1-14, 2020.

Diermeier, D. and Li, C., Electoral control with behavioral voters, The Journal of Politics, 79(3), pp. 1-33, 2017.

Bernard, S., Bouza, G. and Pietrus, A., An optimal control approach for E-rumor, Revista Investigacion Operacional, 36(2), pp. 108-114, 2014.

Rachik, Z., Labzai, A., Balatif, O. and Rachik, M., A multi-region discrete-time mathematical modeling and optimal control of an electoral behavior, Journal of Mathematical and Computational Science, 10(6), pp. 2579-2598, 2020.

Sofia, I.R. and Ghosh, M., Mathematical modeling of smoking habits in the society, Stochastic Analysis and Applications, 41(5), pp. 918-937, 2023.

Mart?nez-Far?as, F.J., Alvarado-Sanchez, A., Rangel-Cortes, E. and Hernandez-Hernandez, A., Bi-dimensional crime model based on anomalous diffusion with law enforcement effect, Mathematical Modelling and Numerical Simulation with Applications, 2(1), pp. 26-40, 2022.

Akanni, J.O., Akinpelu, F.O., Olaniyi, S., Oladipo, A.T. and Ogunsola, A.W., Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis, International Journal of Dynamics and Control, 8, pp. 531-544, 2020.

Sher, M., Shah, K., Sarwar, M., Alqudah, M.A. and Abdeljawad, T., Mathematical analysis of fractional order alcoholism model, Alexandria Engineering Journal, 78, pp. 281-291, 2023.

Dokuyucu, M.A., A fractional order alcoholism model via Caputo-Fabrizio derivative, AIMS Mathematics, 5(2), pp. 781-797, 2020.

Soewono, E., On the analysis of Covid-19 transmission in Wuhan, Diamond Princess and Jakarta-cluster, Communication in Biomathematical Sciences, 3(1), pp. 9-18, 2020.

Syrti, B.M., Devi, A. and Kashyap, A.J., Analysis of stability, sensitivity index and hopf bifurcation of eco-epidemiological SIR model under pesticide application, Communication in Biomathematical Sciences, 6(2), pp. 126-144, 2023.

Muthu, P. and Bikash, M., Study of a delayed SIVA within-host model of dengue virus transmission, Communications in Biomathematical Sciences, 5(2), pp. 101-120, 2022.

Musafir, R.R., Suryanto, A. and Darti, I., Dynamics of COVID-19 epidemic model with asymptomatic infection, quarantine, protection and vaccination, Communication in Biomathematical Sciences, 4(2), pp. 106-124, 2021.

Darti, I., Suryanto, A., Panigoro, H.S. and Susanto, H., Forecasting COVID-19 epidemic in Spain and Italy using a generalized Richards model with quantified uncertainty, Communication in Biomathematical Sciences, 3(2), pp. 90-100, 2020.

Ndii, M.Z., Beay, L.K., Anggriani, N., Nukul, K.N. and Djahi, B.S.,Estimating the time reproduction number in Kupang City Indonesia, 2016?2020, and assessing the effects of vaccination and different Wolbachia strains on dengue transmission dynamics, Mathematics, 10(12), p. 2075, 2022.

Beay, L.K. and Anggriani, N., Dynamical analysis of a modified epidemic model with saturated incidence rate and incomplete treatment, Axioms, 11(6), p. 256, 2022.

Beay, L.K., Modelling the effects of treatment and quarantine on measles, AIP Conference Proceedings, 1937(1), 2018.

Marsudi, T., Suryanto, A. and Darti, I., Global stability and optimal control of an HIV/AIDS epidemic model with behavioral change and treatment, Engineering Letters, 29(2), pp. 575-591, 2021.

Safi, M.A., Global stability analysis of two-stage quarantine-isolation model with Holling type II incidence function, Mathematics, 7(4), p. 350, 2019.

Dang, Q.A. and Hoang, M.T., Positivity and global stability preserving NSFD schemes for a mixing propagation model of computer viruses, Journal of Computational and Applied Mathematics, 374, p. 112753, 2020.

Huo, H.F. and Zou, M.X., Modelling effects of treatment at home on tuberculosis transmission dynamics, Applied Mathematical Modelling, 40(21-22), pp. 9474-9484, 2016.

Ullah, I., Ahmad, S., Al-Mdallal, Q., Khan, Z.A., Khan, H. and Khan, A., Stability analysis of a dynamical model of tuberculosis with incomplete treatment, Advances in Difference Equations, 499, pp. 1-14, 2020.

Lopez-Moctezuma, G., Wantchekon, L., Rubenson, D., Fujiwara, T. and Pe Lero, C., Policy deliberation and voter persuasion: Experimental evidence from an election in the Philippines, American Journal of Political Science, 66(1), pp. 59-74, 2022.

Solhaug, T. and Christophersen, K.A.A., Political awareness, concept and measurement, Perspectives on Political Awareness: Conceptual, Theoretical and Methodological Issues, pp. 35-56, 2022.

Gattermann, K. and de Vreese, C., Awareness of Spitzenkandidaten in the 2019 European elections: The effects of news exposure in domestic campaign contexts, Research and Politics, pp. 1-8, 2020.

Waldvogel,T., Konig, P.D. and Wagschal, U., All I do is win, no matter what? What matters in gaining electoral support from televised debates, Communication and Society, 36(1), pp. 127-149, 2022.

Oswald, S., Pragmatics for argumentation, Journal of Pragmatics, 203, pp. 144-156, 2023.