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All Journal BAHASA DAN SASTRA Katalogis AGRISAINS Media Eksakta Jurnal Ilmu Kedokteran (Journal of Medical Science) Factum: Jurnal Sejarah dan Pendidikan Sejarah Jurnal Online Mahasiswa (JOM) Bidang Keguruan dan Ilmu Pendidikan CEMARA EDUNOMIC : JURNAL ILMIAH PENDIDIKAN EKONOMI FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN Wardah JURNAL KOLABORASI Jurnal Al-Qadau: Peradilan dan Hukum Keluarga Islam JURNAL KEGURUAN Majalah Kedokteran Sriwijaya Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) INTEGER: Journal of Information Technology Resona : Jurnal Ilmiah Pengabdian Masyarakat Jurnal Geografi Jurnal Ekonomi Bisnis Syariah ICoTE Proceedings Jurnal Pendidikan Kebutuhan Khusus Jurnal BIOEDUIN : Program Studi Pendidikan Biologi SEIKO : Journal of Management & Business Etika Demokrasi Journal of Islamic Nursing Gorontalo Agriculture Technology Journal JMM UNRAM (Jurnal Magister Manajemen Universitas Mataram) Jurdimas (Jurnal Pengabdian Kepada Masyarakat) Royal JURNAL GLOBAL EDUKASI Edumaspul: Jurnal Pendidikan Logista: Jurnal Ilmiah Pengabdian Kepada Masyarakat YUME : Journal of Management Jurnal Agregasi APPROACH: Jurnal Teknologi Penerbangan Menara Ilmu JURNAL ILKES (Jurnal Ilmu Kesehatan) Edukasia : Jurnal Pendidikan Abdimas Universal Judika (Jurnal Nusantara Medika) PRAJA: Jurnal Ilmiah Pemerintahan Contemporary Mathematics and Applications (ConMathA) Jurnal Al-Amin: Kajian Pendidikan dan Sosial Kemasyarakatan Community Development Journal: Jurnal Pengabdian Masyarakat JDP (Jurnal Dinamika Pemerintahan) Budapest International Research and Critics Institute-Journal (BIRCI-Journal): Humanities and Social Sciences Jurnal Pendidikan Dasar dan Keguruan Lingua Rima: Jurnal Pendidikan Bahasa dan Sastra Indonesia AGRISCIENCE KIDDO: Jurnal pendidikan Islam Anak Usia Dini Akrab Juara : Jurnal Ilmu-ilmu Sosial Jurnal AgroSainTa: Widyaiswara Mandiri Membangun Bangsa Indobiosains Jurnal Ilmiah Wahana Pendidikan Al-Maraji': Jurnal Pendidikan Bahasa Arab JRMB (JURNAL RISET MANAJEMEN & BISNIS) Borneo Journal of Biology Education (BJBE) Biopedagogia International Journal of Humanities Education and Social Sciences Jurnal Pendidikan dan Sastra Inggris (JUPENSI) Kusa Lawa Jurnal Ilmiah Berkala: Sains dan Terapan Kimia NUSANTARA: Jurnal Pengabdian Kepada Masyarakat VIGOR: JURNAL ILMU PERTANIAN TROPIKA DAN SUBTROPIKA Journal of Training and Community Service Adpertisi e-Jurnal Inovasi Pembelajaran Sekolah Dasar e_Jurnal Ilmiah Riset Akuntansi Wiratani : Jurnal Ilmiah Agribisnis Jurnal Kabar Masyarakat Jurnal Kajian Manajemen Dakwah Al Yazidiy: Jurnal Sosial Humaniora dan Pendidikan Al Itmamiy : Jurnal Hukum Ekonomi Syariah Kreativitas Pada Pengabdian Masyarakat (Krepa) Jurnal Pengabdian Kepada Masyarakat Jurnal Motivasi Pendidikan dan Bahasa Lokawati: Jurnal Penelitian Manajemen dan Inovasi Riset Jurnal Yudistira Muqaddimah: Jurnal Ekonomi, Manajemen, Akuntansi dan Bisnis Bersatu: Jurnal Pendidikan Bhinneka Tunggal Ika Morfologi : Jurnal Ilmu Pendidikan, Bahasa, Sastra dan Budaya Tabsyir: Jurnal Dakwah Dan Sosial Humaniora Khirani: Jurnal Pendidikan Anak Usia Dini Al Itimad: Jurnal Dakwah dan Pengembangan Masyarakat Islam Moneter : Jurnal Ekonomi dan Keuangan Menawan : Jurnal Riset dan Publikasi Ilmu Ekonomi Jurnal Dikmas Jurnal Inovasi Ekonomi Syariah dan Akuntansi Jurnal Intelek Insan Cendikia Jurnal Pendidikan Dasar dan Keguruan EDUNOMIC : JURNAL ILMIAH PENDIDIKAN EKONOMI FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN Jurnal Manajemen Bisnis Digital Terkini Federalisme : Jurnal Kajian Hukum Dan Ilmu Komunikasi Ulil Albab Jurnal Ekonomi, Manajemen Pariwisata dan Perhotelan
Fatmawati Fatmawati
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Journal : Contemporary Mathematics and Applications (ConMathA)

 1 
Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran Muhammad Iqbal Abdi Farchan; Fatmawati Fatmawati; Cicik Alfiniyah
Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 1 (2020)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (706.178 KB) | DOI: 10.20473/conmatha.v2i1.19300

Abstract

Customer dynamics include the exchange of information and ongoing transactions between customers and the organization. This process has an important role in the company to run its business, so that the number of customers increase. To achieve this, many things are done by the company. One of the strategies is product advertising by word of mouth. The purpose of this thesis is to analyze the stability of equilibrium point and to apply the optimal control word of mouth advertising on mathematics model of the customer dynamics based on marketing policy. Mathematics model of the customer dynamics based on marketing policy without control has two equilibrium points, namely non – endemic equilibrium (E0) and endemic equilibrium (E1). Local stability of equilibrium and the existence of endemic equilibrium depends on basic reproduction number (R0). The non – endemic equilibrium tend to asymptotically stable if R0 < 1.  The problem of optimal control is solved by Pontryagin’s Maximum Principle. The simulation results show that the total number of referral and regular customer populations that are given control in the form of word of mouth advertising efforts at the end of the observation are 312 and 18470 with the control effort costs occurred in 1798364.63. While the total number of referral and regular customer populations that are not given control in the form of word of mouth advertising efforts at the end observation are 241 and 17260. Based on these results show that word of mouth advertising efforts have an effect to increase the number of referral and regular customer in accordance with the aim of providing optimal control.
Co-Authors Abd Rahim Razaq Abd. Herman Syah Thalib Abd. Rahim Arsyad Abd. Rahman Abdul Jabbar Tahir Abi Wahyu Rosabi Abidin Abidin Abu Sofyan Achmad Agus Priyono Achmad Musyahid Achmad Risdiyanto Afifah Istiqomah Afpriyanto Afpriyanto Agung Widhi Kurniawan Ahmad Budi Junaidi Ahmad Syahid Aisyah Syarifuddin Al Fina Kusuma Putri Alfiniyah, Cicik Aminah Aminuddin Aminuddin Amiruddin . Amzaq Bagus Purnomo Ana Merdekawati Ananda Mar’atus Sholikhah Andi Jayanti Andi Liswahyuni Andi Muhibuddin Andi Mustika Amin Andi Nur Auliya Andi Nur Wahyuningsih Andini Aprilia Ardhana Andrie Chaerul ANNISA SALSABILA Anwar Anwar Anwar Ramli Anwar, Anas Iswanto Ardinal Ardinal Arif Wahyu Nugroho Aspitriani Astri Widyaruli Anggraeni Asura Useng Baharuddin Baharuddin Baharudin Ardani Bayu Permana Putra Bunga Dwi Yuliana Caska - Chandra Ayu Pancalara Sakti Chandra Wijaya Chandra Wijaya Cicit Mahmut Cucu Irma Firnanda Danang Yonarta Darmais Darmais Delfia Resti Amalia Desak Made Ristia Kartika Devi Undhatuz Zulfa Dita Puspita Junaedi Diyan wahyuningsih Djuliati Saleh Dody Tri Kurniawan Dyah Siswanti E eikke eikke Ekajayanti Kining Ester Julinda Simarmata, Ester Julinda Evi Roviati Faisal Eka Mahendra Faiz Faiz Faoyan Agus Furyanto Febi Cahyani Febrina Dafit, Febrina Ferdinan Yohanes Fony Marcelia Ghozali Ghozali Gigih Ardiansyah Suwarsono Gimin Gimin Gustia Haryati Habil Abdillah Harti Budi Haryana Gani Hasmiati Hasmiati Henny Dianawati Hilda Andini Mandasari Historiawati Historiawati Husni Watul Hasanah Ihyani Malik Ika Mayasari Irfannuddin Irfannuddin Ismail Ismail Ita Sarmita Samad Ivana Magdalena Jaelan Usman Jamaluddin Al Afgani Jeferson Boling Juhandi Juhandi Junia Amalia K Soewardi Karmala Karmala Karmila Achmad Kartika Kartika khaeriah Muh Diar Khaerunnisa Khaerunnisa Khairil Ansar Kris Uluelang Kundharu Saddhono Kurnianti Alexander L Adrianto Lady Silk Moonlight Laila Rochmawati Lailul Muqaromah Laksono Trisnantoro Listiani Listiani Loli Safitri M. Ikhsanul Fikri M. Miftahur Rahmat Isnaini Madris Madris Mahmud Mahmud Mariatul Kiptiah Marlina Marlina Mauiza Al-Mawaddah Medina Athiah Mijani Rahman Mirna Fitrani Moh. Amin Moh. Amin Mohammad Anwar Muh Yusuf Muh. Ilham Azis Muhamad Zen Muhammad Hanif Fandi Muhammad Imaduddin As&#039;ad Muhammad Iqbal Abdi Farchan Muhammad Qadaruddin Muhammad Ridwansyah Muhammad Syaiful Muhammad Yudha Ardiansyah Muhlis Madani, Muhlis Musdalifah Musdalifah Nadiroh Nadya Pradita Hosensyah Nafis Syafaatul Awaliyah Nasruni Nasruni Nida’ Nur Anisah Noe Komari Nova Putri Ramadhani Nur Aina Nur Chamidah Nur Fadilah Amin Nuraeni Nuraeni Nurliani Nurliani Nurshakila Nurshakila Nursia Nursia Nurul Azmy Rustan Nurwahidah Marzuki Purwati Ratna Wahyuni Puspa Dewi Amanda R. A. Delila Tsaniyah Ramadan Ramadan Ramin Ode Ratna Ratna Raysa Nurul Diva Reflinda, Reflinda Retno Cahya Mukti Rezki Maulina Ricksen Sonora Roffies Ricky. Z Rika Handiyani Rini Yana Rinto Astutik Rochmawati, Laila Romansyah Sahabuddin Rusli Abdullah Rustiani Rustiani Sadakata Sinulingga Safiq Al-Kalam Safyudin Sahriani Sahriani Saiman Sutanto Saini Salfius Seko Santika Oktavian Sarah Nuraini Wahyudi Satria Zanu Kurniawan Selvia Marcelina Selvieni Selvieni Selvina Dewi Anggraini Setiawati Setiawati Shultan Alif Firmansyah Sintya Meirna Eka Putri Siti Hardianti Siti Maizul Habibah Siti Nurhalizah Siti Sofiah Rahmawati Sobar Sutisna Sri Gustina Pane Suarman Suarman Subandrate Sudarsana Arka Sukma, Meita Maharani Sulaeman Masnan Susilawati Susilawati Suyanto Suyanto Syahril Syawal Syahrul Syahrul Syarah Rama Syahfitri T Kusumastanto Tarunasena Ma&#039;moer Tasnim Tasnim Teguh Arifianto Tina Oktarina Toha Saifudin Totok Sulistyo Trismadi Trismadi Vlorensius Vlorensius Wahdania Wahdania Wahyu Linggar Pamuji Widia Herdianti Yasinta Najwa Yayah Badriyah Yohanes Bahari Yukir Yukir Yulia Eko Susilowati Yulinar Yulinar Zulfadli Zulfadli Zulham Sirajuddin