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All Journal Journal of the Indonesian Mathematical Society Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Rizka, Sailah Ar
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Computer Science & IT Mathematics

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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.
Co-Authors Afli, Febrianto Ayu, Regina Wahyudyah Sonata Dewi Ika Ainurrofiqoh Kholifia, Nadia Regina Wahyudyah Sonata Ayu Sari, Merysa Puspita Wilda, Robiatul Witari Yumia, Mega