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Journal : Jambura Journal of Biomathematics (JJBM)

Comparison of Fractional-Order Monkeypox Model with Singular and Non-Singular Kernels Musafir, Raqqasyi Rahmatullah; Suryanto, Agus; Darti, Isnani; Trisilowati, Trisilowati
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.24920

Abstract

The singularity of the kernel of the Caputo fractional derivative has become an issue, leading many researchers to consider the Atangana-Baleanu-Caputo (ABC) fractional derivative in epidemic models where the kernel is non-singular. In this context, the objective of this study is to compare the calibration and forecasting performance of fractional-order monkeypox models with singular and nonsingular kernels, represented by the model with respect to the Caputo operator and the ABC operator, respectively. We have proposed a monkeypox epidemic model with respect to the ABC operator (MPXABC), where the model with respect to the Caputo derivative (MPXC) has been proposed in previous research. We have analyzed the existence and uniqueness of the solution. Three equilibrium points of the model are endemic, human endemic, and monkeypox-free, and their global stability has been investigated. The global dynamics of the MPXABC are the same as those of the MPXC. In evaluating the performance, we collected secondary data on weekly monkeypox cases from June 1 to November 23, 2022, in the USA. Parameter estimation has been performed using the least squares method, while the solutions of the model have been determined numerically using a predictor-corrector scheme. The benchmark for performance has been determined based on the root mean square error. Data calibration and forecasting indicate that the MPXC generally has the best performance for each value of the derivative order. For certain values of derivative order, the MPXABC performs better than the corresponding firstorder model. However, generally, the corresponding first-order model performs better than the MPXABC. Depending on the data trends and the specified orders, the MPXC outperforms the MPXABC. Thus, the singularity issue of the Caputo derivative does not always have a negative impact on model fitting to data.
The Dynamics of a Predator-Prey Model Involving Disease Spread In Prey and Predator Cannibalism Ah, Nurul Imamah; Kusumawinahyu, Wuryansari Muharini; Suryanto, Agus; Trisilowati, Trisilowati
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.21495

Abstract

In this article, dynamics of predator prey model with infection spread in prey and cannibalism in predator is analyzed. The model has three populations, namely susceptible prey, infected prey, and predator. It is assumed that there is no migration in both prey and predator populations. The dynamical analysis shows that the model has six equilibria, namely the trivial equilibrium point, the prey extinction point, the disease free and predator extinction equilibrium point, the disease-free equilibrium point, the predator extinction equilibrium point, and the coexistence equilibrium point. The first equilibrium is unstable, and the other equilibria conditionally local asymptotically stable. The positivity and boundedness of the solution are also shown. The analytical result is supported by numerical simulation. It is shown that in such a high cannibalization the coexistence equilibrium is locally asymptotically stable.
Co-Authors A Halim A.A. Ketut Agung Cahyawan W A’yun, Norma Qurrota Abrianti, Putri Achmadi, Taofan Ali Addieni, Mulia Addin, Muhammad Faqih Adenita Cynthia Affan, Banu Nur Agus Murnomo Aini Nurul Ainurrasjid Ainurrasjid Ainurrasyid Ainurrasyid Aji, Mukhammad Wildan Akbar, Mohammad Fani Alislami, Tia Candra Khaula Amellia Firdaus Zahra Anan Nugroho Andy Andy Angelia Norma Wulandari Anggraini Mulwinda Anggraini Mulwinda Apriyanto, Eko Bagus Arfriandi, Arief Arif Budi Prasetya Ashar, Fauzi Asriningati Asriningati Bahrul Maani Bangun, Kosa Otaka Cahyani, Agustina Rizky Cahyo Fajar Adhiningtyas Chaerunnisa, Chaerunnisa Chaerunnisa, Sita Sarah Daffa, Muhammad Abu Damaiyanti, D. R. R. Damaiyanti, D.R.R. Damanik, Jhones King Damanik, Sariah Aprianti Darmawan, Krisna Reza Darmoyo Darmoyo Dendy Eta Mirlana Dewi Ratih Rizki Damaiyanti Dewi, Nur Afifah Dewi, Wening Tiara Dhidik Prastiyanto Diah Ayu Kusumawati Diah Ayu Kusumawati Didik Hariyono Diyoprakuso, First Djallalluddin Djallalluddin Dyah Erlina Sulistyaningrum Edy Prayitno Eko Supraptono Eko Widaryanto Eline, Merina Endang Wuryandini Erika Tinambunan Erlambang, Rere Erviani, Diah Erviani, Diah Fahrurrozy, Mohammad Farida Farida Febrianti, Annisa Fitri Feddy Setio Pribadi Ferdian, Herman Ferry Fauzi, Ferry Fikrie Rizqy Juan Bismaditya Firdaus, Mohammad Nur Firokhman, Alnguda Fita Anggraini Friska Rizqi Pratiwi Gestiyana Ayu Kurnia Puteri Girsang, Srimayanti Hadinata, Nadia Agus Hanang Wibisono, Banteng Handoyo, Thomas Hari Wibawanto Hasan S. Panigoro Hemida Kusumaningrum Heriana, Tutik Hirlan Hirlan Huda, Mukhammad Robitul Hudallah, Nur Husni Thamrin Sebayang Ibrahim M. H. Sanhoury Ilmam, Hasbi Shidqi Indrawan, Rahadyan Rizki Indriyani, Triska Widya Inovian Wahyuningsih, Inovian Ismail, Moch. Taufiq Isnani Darti Jatumara, Prawesty Dinnar Juprianto, Miki Kartono - Karuniawan Puji Wicaksono Khoiril Anam, Khoiril Khoirudin Fathoni, Khoirudin Khotimah , Khusnul Koesriharti Koesriharti Krisnawati, Vira Hari Kumalasari, Septi Nuning Kurniawan, Berry Kusumaningtyas, Sa'aprita Kusumawinahyu, W. M. Lilik Setyobudi Lutfiyana, Lutfiyana M. Harlanu, M. Mai Puspadyna Bilyastuti Maitimu, Dyah Kartika Mario Norman Syah, Mario Norman Marsela, Marsela Matanari, Dimpo Cicio Matatula, Denis Andre Medha Baskara Misromi, Misromi Mochammad Dawam Maghfoer Mochammad Samsul Arifin Mochammad Wildan Nugraha Moh. Amin Mohammad Ainun Multazam Mubarok, Ahnan Mudhofi Nurrohman Mudji Santosa Muhammad Akmal Muhammad Luthfi Muhtadi, Much Misbah Musafir, Raqqasyi Rahmatullah Nafiah, Vivi Imroatin Najma Aulia Nakhmiidah, Nisa Nararya, Mas Bagus Aulia Nia Kurniawan Nindra, Daffa Ninuk Herlina Nobukazu Nakagoshi Noor Hudallah Noor Ramadhan, Akbar Noor, Arifin Nugraha, Alfikri Raihan Nugraha, Hanggara Dwiyudha Nugroho, Agung Nur Hidayat Nuri Aulya Nurkhanifah, Nia Nurkharisma, Aditya Nurkholis, Fathur Nurlaelih, Euis Ellih Nurul Imamah Octavianti Paramita Oscar Regazzoni Pambudi, Muhammad Ario Paramyta Nila Permanasari, Paramyta Nila Pranata, Bayu Ari Pranata, Bayu Ari Prastika, Angrenani Rindu Prayitno, Marco Ferrianto Prayoga, Kharisma Marta Prihatin, Lilik Purnomo, Anna Silvia Putri Andriani Putri, Fadhila Ravinda R Kartono, R Rahman, Antony Anwari Rahmawati, Anindya Ramadhan, Apianto Rizky Ramadhana, Syahrul Raunica, Elsha Afry Rayungsari, Maya Resmawan Resmawan Reza Ardian Wahyu Ramadhan, Reza Ardian Riana Defi Mahadji Putri Ridwan, Dzaky Fakhriza Rinata, Mar’atus Eski Riza Fitriani, Riza Rizky Rachmadi Utomo Roedy Soelistyono Ruslan Abdul Gani Saptariana - Saptriana Suryanto, Saptriana Saputra, Handika Lintang Seftriana Anifa Khusniasari Setio, Pradipa Setyono Yudo Tyasmoro Setyono, Bagus Wahyu Setyowati Pertiwi, Indah Shafakamila, Salsabila Nazla Shelvi Sellitasari Sholeh, Mohammad Hasyim Sianturi, Michael Fias Sidabutar, Malkia Hotman Simbolon, Santri Novalina Sisca Fajriani Sitawati Sitawati Sitawati, . Sri Puji Lestari Sri Sartono, Sri Sri Sukamta Suchaida, Azziyaa Suci Surya Dewi Sudiarso Sudiarso Sugeng Sugeng Suhatman, Yan Sunaryo Sunaryo Suwasono Heddy Syahrul Ramadhan Tanamas, Jimmy Tarigan, Maulana Ikhsan Tatyantoro Andrasto Tia Anggara, Dewi Shinta Tindriyani, Niswatul Arifah Titin Sumarni Toto Himawan Tri Rahayuningsih Trisilowati Trisilowati, Trisilowati Tristi Indah Dwi Kurnia Tyary Airivia Udayana, Cicik Ulfah Mediaty Arief Uswatun Hasanah Utomo, M. Dika Cahyo Utomo, Yosafat Rio Wardhani, Dyah Ayu Kusuma Warma, Mohammad Perdana Prehatama Putra Wibowo, Ario Wahyu Wicaksono, Dwi Haryo Wiwin Sumiya Dwi Yamika, Wiwin Sumiya Wulandari, Dania Ayu Wulansari, Atikah Wuryasari Muharini Kusumawinahyu Yoga Oktavianto Yogi Sugito Yoom, Lilis Irjayanti Yuniaratri, Riris Yuniaratri, Riris Yusuf, Dedi Yuwono, Amrih Zuanita, Reni