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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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Dynamics of Lumpy Skin Disease Model With Vaccination and Environmental Transmission Nia Nurkhanifah; Agus Suryanto; Isnani Darti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29969

Abstract

Lumpy skin disease (LSD) is one of the cattle diseases that can spread rapidly, it is caused by lumpy skin disease virus (LSDV). LSDV can spread through direct contact, insect vectors, and contaminated environments. In this article, we propose the dynamics of a lumpy skin disease model that contains seven compartments: susceptible cattle, vaccinated cattle, infected cattle, recovered cattle, susceptible vector, infected vector, and LSDV in the environment. The non-negativity and boundedness of the solution of the proposed LSD model are shown. There are two equilibrium points: the disease-free equilibrium point which always exists, and the endemic equilibrium point which exists conditionally. The disease-free equilibrium point is locally and globally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium is locally asymptotically stable if the Lienard-Chipart criteria is satisfied. In addition, based on the sensitivity analysis, we find that the vaccination rate is the most sensitive parameter. All analytical results have been verified by our numerical simulations.
Pricing Double Barrier Options with Time-Varying Interest using Standard, Antithetic, and Control Variate Monte Carlo Bella Cindy Thalita; Isnani Darti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.37010

Abstract

This study develops an integrated framework for pricing double barrier options under time-varying interest rates by combining ARIMA-based forecasting with Monte Carlo simulations. Monthly U.S. Treasury Bill rates from 2019–2025 are modeled using the ARIMA(2,2,0) process to generate dynamic risk-free rates, which are incorporated into three Monte Carlo approaches standard, antithetic variate, and control variate. Tesla Inc. stock prices are used as the underlying asset modeled through Geometric Brownian Motion. The integration of ARIMA-based dynamic rates within the Monte Carlo framework enables more realistic pathwise discounting and improves simulation convergence. The results show that the control variate method provides the most accurate and stable estimates for knock-in call options, whereas the antithetic variate technique yields superior accuracy for knock-in put, knock-out call, and knock-out put options. Overall, the combined use of ARIMA-forecasted interest rates and variance-reduction techniques enhances the precision and stability of double barrier option valuation under dynamic financial conditions.
Co-Authors Agus Suryanto Agus Suryanto AGUS WIDODO Al Fauzi, Abdul Latif Aulani, Fitroh Bella Cindy Thalita Chatarina Umbul Wahyuni Damayanti, Rismania Hartanti Putri Yulianing Darmanto Darmanto Fery Widhiatmoko 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 Nia Nurkhanifah Nurjannah Nurjannah Pratiwi, Fara El Nandhita Purnomo, Anna Silvia Rahmah, Havida Rayungsari, Maya Resmawan Resmawan Saputra, Handika Lintang Sobri Abusini Suci Astutik Suryanto, Agus Syaiful Anam Trisilowati Trisilowati, Trisilowati W.A, Rinda Anggraini Wardani, Cholida Usi Wuryasari Muharini Kusumawinahyu