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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Mathvision : Jurnal Matematika Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Tensor: Pure and Applied Mathematics Journal
Kholifia, Nadia
Universitas Jember
Computer Science & IT Mathematics

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Kontrol Optimal untuk Model Coffee Berry Disease dengan Vektor Pembawa Colletotrichum kahawae: Optimal Control for Coffee Berry Disease Model with Carrier Vector of C. kahawae Rizka, Sailah Ar Rizka; Kholifia, Nadia
MathVisioN Vol 6 No 2 (2024): September 2024
Publisher : Prodi Matematika FMIPA Unirow Tuban

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55719/mv.v6i2.1396

Abstract

Coffee Berry Disease (CBD) is a fungal disease of coffee caused by Colletotrichum kahawae, resulting in significant losses of both quality and quantity of the coffee produced. Optimal control is applied to CBD models where the interaction between carrier vectors and pathogenic fungi is considered. Control strategies include the use of fungicides and biocontrol agents. The optimal control problem is formulated to minimise the cost of implementing the interventions, along with the numbers of infected coffee, pathogenic fungi, and their carrier vectors. The existence of optimal control and the necessary conditions for optimality are solved using Pontryagin's Minimum Principle. The cost-effectiveness of implementing several control strategies was examined using the Incremental Cost-Effectiveness Ratio (ICER). Numerical simulations demonstrate the effectiveness of optimal control in mitigating CBD.
Optimal Control for a COVID-19 and Tuberculosis Co-Infection Model with Asymptomatic COVID-19 Carriers Rizka, Sailah Ar; Ayu, Regina Wahyudyah Sonata; Ainurrofiqoh, Dewi Ika; Sari, Merysa Puspita; Kholifia, Nadia
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 1 April 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i1.31076

Abstract

This study applies optimal control theory to a deterministic co-infection model of COVID-19 and tuberculosis (TB) with asymptomatic COVID-19 carriers, who are assumed to be less infectious. The optimal control strategy aims to minimize intervention costs and reduce infections by implementing five control measures, including prevention and vaccination of COVID-19, treatment of both symptomatic and asymptomatic COVID-19-infected individuals, treatment of COVID-19 and active TB co-infected individuals, and prevention of treatment failure in active TB cases. Pontryagin's minimum principle is used to characterize the necessary conditions for optimal control in reducing infections. Numerical results demonstrate the effectiveness of the optimal control strategy in suppressing diseases. The incremental cost-effectiveness ratio (ICER) for different combinations of control measures is evaluated, showing that the intervention strategy performs best when all control measures are used.
Batas Perturbasi Mutlak Nilai Eigen dari Matriks Normal Ainurrofiqoh, Dewi Ika; Sari, Merysa Puspita; Rizka, Sailah Ar; Kholifia, Nadia
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 2 August 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i2.31084

Abstract

The eigenvalue problem in matrices is an important topic in numerical computation, particularly in analyzing the sensitivity of eigenvalues to disturbances or perturbations. This study discusses the absolute perturbation bounds on the eigenvalues of a matrix, focusing on normal matrices and their relationship to the condition of normal matrices. Based on existing theorems, the absolute perturbation bounds are presented in various forms involving the Frobenius norm and the condition number of the matrix eigenvectors. This research provides a detailed discussion of results concerning the absolute perturbation bounds on eigenvalues and their applications to normal matrices. Ultimately, an important result on the error bounds of eigenvalues in the case of normal matrices affected by perturbations is fully explained, proving the connection between the absolute error bound and the Frobenius norm of the perturbations.
Performance Analysis of Grey Wolf Optimizer for Solving Nonlinear Systems with Complex Roots Merysa Puspita Sari; Dewi Ika Ainurrofiqoh; Agustina Pradjaningsih; Sailah Ar Rizka; Nadia Kholifia
Tensor: Pure and Applied Mathematics Journal Vol 7 No 1 (2026): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol7iss1pp1-8

Abstract

Nonlinear systems of equations consist of multiple equations that must be solved simultaneously, and analytical solutions are often difficult to obtain, particularly for complex cases. For this reason, numerical and metaheuristic approaches are frequently employed as practical alternatives. This study investigates the performance of the Grey Wolf Optimizer (GWO) in solving nonlinear systems involving both real and complex roots. The problem is reformulated as an optimization task by minimizing a modulus based objective function derived from the given system. The implementation is carried out in MATLAB using several test cases, and a parameter sensitivity analysis is conducted with respect to the number of search agents, search boundaries, and maximum iterations. To evaluate its performance, the results obtained using GWO are compared with those of the Particle Swarm Optimization (PSO) algorithm reported in previous studies. The findings indicate that GWO is able to produce stable solutions with objective function values close to zero across different cases. However, PSO tends to achieve higher accuracy and faster convergence in certain scenarios. Despite this, GWO demonstrates strong exploration capability, which contributes to its robustness and makes it a viable alternative for solving complex nonlinear systems.
Macroeconomic Determinants of Investment Credit in Indonesia: Evidence from the ARDL Bounds Testing Approach Nur Atikah; Nadia Kholifia; Lucky Tri Oktoviana; Muhammad Ilham Arif; Muhammad Nizar Hidayatullah; Vagustin Faharani; Mareta Putri Manunggal
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): 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.v11i2.42713

Abstract

Investment credit plays an important role in financing productive activities and sustaining Indonesia's economic development. Nevertheless, limited empirical evidence is available regarding how fluctuations in gold prices together with other macroeconomic indicators influence investment credit during the post-pandemic period. This study investigates the effects of gold prices, the USD/IDR exchange rate, the Industrial Production Index (IPI), the BI 7-Day Reverse Repo Rate, and inflation on investment credit using monthly observations from June 2016 to December 2024. An Autoregressive Distributed Lag (ARDL) model combined with an Error Correction Model (ECM) is employed to evaluate both long-run associations and short-run adjustments. The empirical findings reveal that the variables are cointegrated, implying the existence of a stable long-term equilibrium. However, none of the estimated long-run coefficients is statistically distinguishable from zero at conventional significance levels. In the short run, exchange rate movements generate the largest response in investment credit, whereas industrial production and the policy interest rate produce relatively modest effects. The error-correction coefficient is negative and statistically significant, indicating that temporary departures from equilibrium are gradually eliminated over time. These findings suggest that investment credit in Indonesia is driven primarily by short-term macroeconomic adjustments rather than persistent long-run effects of individual macroeconomic variables.
Co-Authors Agustina Pradjaningsih Dewi Ika Ainurrofiqoh Lucky Tri Oktoviana Mareta Putri Manunggal Merysa Puspita Sari Muhammad Ilham Arif Muhammad Nizar Hidayatullah Nur Atikah Regina Wahyudyah Sonata Ayu Rizka, Sailah Ar Vagustin Faharani