Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate
Voter participation in general elections is an important aspect of a democratic state structure. Participation is determined by the level of public political awareness, if the level of public political awareness is low, voter participation tends to be passive (Abstinence). A mathematical model appro...
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| Format: | Article |
| Language: | English |
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Universitas Airlangga
2021-05-01
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| Series: | Contemporary Mathematics and Applications (ConMathA) |
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| Online Access: | https://e-journal.unair.ac.id/CONMATHA/article/view/26939 |
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| author | Dinda Ariska Putri Windarto Windarto Cicik Alfiniyah |
| author_facet | Dinda Ariska Putri Windarto Windarto Cicik Alfiniyah |
| author_sort | Dinda Ariska Putri |
| collection | DOAJ |
| description | Voter participation in general elections is an important aspect of a democratic state structure. Participation is determined by the level of public political awareness, if the level of public political awareness is low, voter participation tends to be passive (Abstinence). A mathematical model approach to voter participation in elections that has been modified to a saturated incidence rate is needed to predict voter participation in future elections. This thesis aims to analyze the stability of the equilibrium point and apply the optimal control variable in the form of an awareness campaign. In the model without control variables, we obtain two equilibriums, namely, the non-endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0), where R0=bL/(g+m)m. There is voter participation in elections when R0 < 1 and the absence of voter participation in elections when R0 > 1. We also analyze the sensitivity of parameters to determine which parameters are the most influential in this mathematical model. Furthermore, the application of control variables in the mathematical model of voter participation in elections with saturated incidence rate is determined through the Pontryagin Maximum Principle method. Numerical simulation results show that providing control variables in the form of awareness campaign it is quite effective in minimize the number of the voting population who abstained from election. |
| format | Article |
| id | doaj-art-663e4aac2bb843c2afcfea8becba73b6 |
| institution | OA Journals |
| issn | 2686-5564 |
| language | English |
| publishDate | 2021-05-01 |
| publisher | Universitas Airlangga |
| record_format | Article |
| series | Contemporary Mathematics and Applications (ConMathA) |
| spelling | doaj-art-663e4aac2bb843c2afcfea8becba73b62025-08-20T02:20:42ZengUniversitas AirlanggaContemporary Mathematics and Applications (ConMathA)2686-55642021-05-0131193510.20473/conmatha.v3i1.2693922039Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence RateDinda Ariska PutriWindarto WindartoCicik AlfiniyahVoter participation in general elections is an important aspect of a democratic state structure. Participation is determined by the level of public political awareness, if the level of public political awareness is low, voter participation tends to be passive (Abstinence). A mathematical model approach to voter participation in elections that has been modified to a saturated incidence rate is needed to predict voter participation in future elections. This thesis aims to analyze the stability of the equilibrium point and apply the optimal control variable in the form of an awareness campaign. In the model without control variables, we obtain two equilibriums, namely, the non-endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0), where R0=bL/(g+m)m. There is voter participation in elections when R0 < 1 and the absence of voter participation in elections when R0 > 1. We also analyze the sensitivity of parameters to determine which parameters are the most influential in this mathematical model. Furthermore, the application of control variables in the mathematical model of voter participation in elections with saturated incidence rate is determined through the Pontryagin Maximum Principle method. Numerical simulation results show that providing control variables in the form of awareness campaign it is quite effective in minimize the number of the voting population who abstained from election.https://e-journal.unair.ac.id/CONMATHA/article/view/26939mathematical modelsoptimal controlsaturated incidence ratestabilityvoter participation. |
| spellingShingle | Dinda Ariska Putri Windarto Windarto Cicik Alfiniyah Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate Contemporary Mathematics and Applications (ConMathA) mathematical models optimal control saturated incidence rate stability voter participation. |
| title | Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate |
| title_full | Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate |
| title_fullStr | Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate |
| title_full_unstemmed | Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate |
| title_short | Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate |
| title_sort | analisis kestabilan dan kontrol optimal model matematika partisipasi pemilih pada pemilihan umum dengan saturated incidence rate |
| topic | mathematical models optimal control saturated incidence rate stability voter participation. |
| url | https://e-journal.unair.ac.id/CONMATHA/article/view/26939 |
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