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All Journal Journal of the Indonesian Mathematical Society Mathvision : Jurnal Matematika Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Tensor: Pure and Applied Mathematics Journal
Rizka, Sailah Ar
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.
Optimal Control of HIV/AIDS Epidemics: Integrating Media Awareness and Antiviral Treatment Ayu, Regina Wahyudyah Sonata; Wilda, Robiatul Witari; Rizka, Sailah Ar; Yumia, Mega; Afli, Febrianto
Journal of the Indonesian Mathematical Society Vol. 31 No. 4 (2025): DECEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i4.1918

Abstract

This paper investigates an optimal control strategy to mitigate the spread of HIV/AIDS by integrating media awareness campaigns and antiviral treatment efforts. A modified SI-type model is developed, dividing the population into five subgroups: unaware susceptible individuals, aware susceptible individuals, unaware infected individuals, aware infected individuals, and individuals undergoing treatment. Additionally, a separate compartment representing the level of media awareness is included to model the dynamics of awareness campaigns over time. Three control variables are introduced: the success of media awareness programs aimed at reducing contact between susceptible and infected individuals and encouraging infected individuals to seek and receive treatment; the effort to provide antiretroviral treatment; and the effort to strengthen the intensity of media awareness programs. The objective is to minimize the number of unaware susceptible and infected individuals while maximizing the number of individuals receiving treatment, and to reduce implementation costs. The model employs optimal control theory to identify the best combination of strategies by minimizing a cost functional. Numerical simulations explore seven control strategy combinations, ranging from single to multiple controls. The results indicate that combining all control variables yields the most significant reduction in unaware and infected individuals, a substantial increase in the number of individuals receiving treatment, and effective minimization of costs.
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.
Co-Authors Afli, Febrianto Agustina Pradjaningsih Ayu, Regina Wahyudyah Sonata Dewi Ika Ainurrofiqoh Kholifia, Nadia Merysa Puspita Sari Regina Wahyudyah Sonata Ayu Wilda, Robiatul Witari Yumia, Mega