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All Journal IAES International Journal of Artificial Intelligence (IJ-AI) The Journal of Experimental Life Sciences (JELS) CAUCHY: Jurnal Matematika Murni dan Aplikasi Bulletin of Electrical Engineering and Informatics Jurnal Mahasiswa Matematika Jurnal Optimasi Sistem Industri Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Communication in Biomathematical Sciences Indonesian Journal of Electrical Engineering and Computer Science Jambura Journal of Biomathematics (JJBM) Tri Dharma Mandiri: Diseminasi dan Hilirisasi Riset Kepada Masyarakat (Jurnal Pengabdian Kepada Masyarakat)
Isnani Darti
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, University Of Brawijaya, Jl. Veteran Malang 65145, Indonesia
Biochemistry, Genetics & Molecular Biology Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Health Professions Immunology & microbiology Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Medicine & Pharmacology Neuroscience Physics Public Health Social Sciences Transportation

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Perambatan Gelombang Optik pada Grating Sinusoidal dengan Chirp dan Taper Darti, Isnani
CAUCHY Vol 1, No 1 (2009): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (379.582 KB) | DOI: 10.18860/ca.v1i1.1697

Abstract

Artikel ini membahas model perambatan gelombang optik pada grating sinusoidal takhomogen. Model tersebut diturunkan dengan mereduksi secara eksak persamaan Helmholtz menjadi sistem persamaan diferensial orde satu dengan syarat awal yang dapat diselesaikan dengan metode Runge-Kutta orde empat. Metode ini disebut Metode IntegrasiLangsung (MIL). Formulasi MIL sangat sederhana baik dalam hal penurunannya maupun implementasinya karena tidak memerlukan prosedur iterasi maupun optimasi. Denganmenggunakan MIL, dipelajari perubahan respon optik pada grating sinusoidal akibat variasi amplitudo modulasi indeks (taper) dan variasi frekuensi spasial grating (chirp). Hasil simulasi menunjukkan bahwa taper menyebabkan adanya fenomena penghilangan side-lobe pada spektrum transmitansi. Adanya chirp menyebabkan penghalusan side-lobe pada spektrum transmitansi dengan semakin besar parameter chirp menyebabkan peningkatan transmitansi di sekitar pusat band-gap dari grating homogen. Selain implementasi integrasi numerik (Runge-Kutta), MIL merupakan metode eksak sehingga dapat digunakan untuk mengevaluasi validitas metode yang sering digunakan yaitu Persamaan Moda Tergandeng (PMT). Dari hasil perbandingan dapat disimpulkan bahwa secara umum PMT kurang akurat dalam menganalisis struktur grating sinusoidal baik homogen maupun tak-homogen.
KEUNTUNGAN RETAILER BERDASARKAN SIKLUS ORDER DAN KEUNTUNGAN BANK OPTIMAL Rahmah, Havida; Darti, Isnani
Jurnal Mahasiswa Matematika Vol 3, No 1 (2015)
Publisher : Jurnal Mahasiswa Matematika

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Abstract

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ANALISIS MODEL ANTRIAN M/M/c/c DENGAN RENEGING BERTIPE R_EOS (RENEGING TILL END OF SERVICE) W.A, Rinda Anggraini; darti, isnani
Jurnal Mahasiswa Matematika Vol 3, No 4 (2015)
Publisher : Jurnal Mahasiswa Matematika

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Abstract

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Forecasting COVID-19 Epidemic in Spain and Italy Using A Generalized Richards Model with Quantified Uncertainty Isnani Darti; Agus Suryanto; Hasan S. Panigoro; Hadi Susanto
Communication in Biomathematical Sciences Vol. 3 No. 2 (2020)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2020.3.2.1

Abstract

The Richards model and its generalized version are deterministic models that are often implemented to fit and forecast the cumulative number of infective cases in an epidemic outbreak. In this paper we employ a generalized Richards model to predict the cumulative number of COVID-19 cases in Spain and Italy, based on available epidemiological data. To quantify uncertainty in the parameter estimation, we use a parametric bootstrapping approach to construct a 95% confidence interval estimation for the parameter model. Here we assume that the time series data follow a Poisson distribution. It is found that the 95% confidence interval of each parameter becomes narrow with the increasing number of data. All in all, the model predicts daily new cases of COVID-19 reasonably well during calibration periods. However, the model fails to produce good forecasts when the amount of data used for parameter estimations is not sufficient. Based on our parameter estimates, it is found that the early stages of COVID-19 epidemic, both in Spain and in Italy, followed an almost exponentially growth. The epidemic peak in Spain and Italy is respectively on 2 April 2020 and 28 March 2020. The final sizes of cumulative number of COVID-19 cases in Spain and Italy are forecasted to be at 293220 and 237010, respectively.
Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination Raqqasyi Rahmatullah Musafir; Agus Suryanto; Isnani Darti
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.3

Abstract

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V ). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points.
Dynamical Analysis and Parameter Estimation of Hepatitis B Disease Model in Malang Fitroh Aulani; Wuryansari Muharini Kusumawinahyu; Isnani Darti
The Journal of Experimental Life Science Vol. 11 No. 3 (2021)
Publisher : Postgraduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.jels.2021.011.03.03

Abstract

In this article, a model representing the spread of Hepatitis B disease is constructed as a nonlinear autonomous system. The model divides the considered human population into three classes, namely susceptible, infected, and recovered class. The dynamical analysis shows that there are two equilibrium points in the model, namely a disease-free equilibrium point and an endemic equilibrium point. The existence and stability of the equilibrium points depend on the basic reproduction number (R_0). The disease-free equilibrium point is local asymptotically stable when R_0<1 while the endemic equilibrium point exists and is local asymptotically stable if R_0>1. The five parameters of the model are estimated by applying Downhill Simplex (Nelder-Mead) Algorithm and by using the infected data cases taken from such a hospital in Malang. The estimated parameters are the transmission of infection rate, the saturation rate, the vaccination rate, the recovery rate, and the immunity loss rate. The resulting parameter estimation supports the analytical result and is used to illustrate the analytical results numerically. Based on the considered model and the result of the parameters estimation, it can be concluded that the Hepatitis B spread in Malang is controllable. Keywords: downhill simplex (Nelder-mead) algorithm, dynamical analysis, hepatitis B model, parameter estimation. 
A Skema Numerik Nonstandar untuk Model Predator-prey dengan Kanibalisme dan Perlindungan pada Predator Rayungsari, Maya; Suryanto, Agus; Kusumawinahyu, W. M.; Darti, Isnani
Communication in Biomathematical Sciences Vol. 6 No. 1 (2023)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2023.6.1.2

Abstract

In this study, we implement a Nonstandard Finite Difference (NSFD) scheme for a predator-prey model involving cannibalism and refuge in predator. The scheme which is considered as a discrete dynamical system is analyzed. The performed analysis includes the determination of equilibrium point and its local stability. The system has four equilibrium points, namely the origin, the prey extinction point, the predator extinction point, and the coexistence point, which have exactly the same form and existence conditions as those in continuous system. The local stability of each first three equilibrium points is consistent with the one in continuous system. The stability of the coexistence point depends on the integration time step size. Nevertheless, the NSFD scheme allows us to choose the integration time step size for the solution to converge to a feasible point more flexible than the Euler and 4th order Runge-Kutta schemes. These are shown via numerical simulations.
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.
Dynamical Analysis of Discrete-Time Modified Leslie-Gower Predator-Prey with Fear Effect Purnomo, Anna Silvia; Darti, Isnani; Suryanto, Agus; Kusumawinahyu, Wuryansari Muharini
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26515

Abstract

It has been studied that fear plays a significant role in establishing ecological communities, influencing biodiversity, and preserving ecological balance in predator-prey interactions. In this study, it is proposed a discrete-time predator-prey model that takes the fear effect into account that is derived by using Euler method. Objective of this study is analyzing the model by linearization. Similar to the continuous model properties, the trivial fixed point and the predator-free fixed point are both unstable. The discrete model differs from the continuous model in that the stability of the interior fixed point and the free prey fixed point is affected by the time step size. Using numerical methods, we examine period-doubling bifurcations related to interior fixed point and prey-free point that are impacted by time step size.
Integrated Pest Management Model with Natural Enemy and Pest-Harvesting Luthfi, Muhammad; Suryanto, Agus; Darti, Isnani
The Journal of Experimental Life Science Vol. 15 No. 1 (2025)
Publisher : Graduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.jels.2025.015.01.03

Abstract

This research aims to develop a mathematical model that describes the dynamics of pests, natural enemies, and refugia plants within the framework of Integrated Pest Management (IPM). The model integrates biological control through predation, mutualistic relationships between natural enemies and refugia plants, and mechanical control through pest harvesting. The proposed model is then analyzed dynamically to study its qualitative behavior. It has been shown that the solutions of the proposed model are non-negative and finite, demonstrating the biological feasibility of the model. We also analyze the local stability of the equilibrium point to gain insight into the system's long-term behavior and to identify conditions that allow effective pest control. We show that the model has seven feasible equilibrium points, but only four of them are stable under certain conditions. In particular, the pest-free equilibrium point is conditionally stable, indicating the potential for effective pest control. Finally, we perform several numerical simulations to confirm the results of our analysis, especially the stability of the four stable equilibrium points. This study provides insight into integrating biological and mechanical strategies in pest management, emphasizing the importance of ecological interactions for sustainable agriculture.   Keywords: integrated pest management, local stability, natural enemy, numerical simulation, refugia plant.
Co-Authors Agus Suryanto AGUS WIDODO Al Fauzi, Abdul Latif Chatarina Umbul Wahyuni Damayanti, Rismania Hartanti Putri Yulianing Darmanto Darmanto Fahrurrozy, Mohammad Fery Widhiatmoko Fitroh Aulani Hadi Susanto Hasan S. Panigoro Irsandy, Diego Khozaimi, Ach. Kusumawinahyu, W. M. Lee, Muhammad Hisyam M.Pd S.T. S.Pd. I Gde Wawan Sudatha . Marsudi Marsudi Muharini Kusumawinahyu, Wuryansari Musafir, Raqqasyi Rahmatullah Nahdhiyah, Ulfatun Nurjannah Nurjannah Nurkhanifah, Nia Pratiwi, Fara El Nandhita Purnomo, Anna Silvia Rahmah, Havida Rayungsari, Maya Resmawan Resmawan Saputra, Handika Lintang Sobri Abusini Suci Astutik Suryanto, Agus Syaiful Anam Thalita, Bella Cindy Trisilowati Trisilowati, Trisilowati W.A, Rinda Anggraini Wardani, Cholida Usi Wuryasari Muharini Kusumawinahyu