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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of Mathematics, Computation and Statistics (JMATHCOS)
Asni, Asriani Arsita
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Mathematics

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Suatu Kajian Tentang B-Aljabar Sanusi, Wahidah; Abdy, Muhammad; Sidjara, Sahlan; Asni, Asriani Arsita
Journal of Mathematics, Computations and Statistics Vol. 3 No. 2 (2020): Volume 03 Nomor 02 (Oktober 2020)
Publisher : Jurusan Matematika FMIPA UNM

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Abstract

This research is a literature studies that aims at reviewing the concepts and properties of B-Algebras. The concept of B-Algebras in this article is based on research that has been done by Neggers and Kim and Allen. All discussions in this article use the firm sets, both finite sets and infinite sets. As a result, more complete evidence of the properties of B-Algebras can be given and its relationship with the group. A group with a specific operation and has as an identity element is a B-Algebras. Moreover, a number of group theorems can be derived into B-Algebra such as natural mapping and the First Isomorphism Theorems which in their proof have similarities to the proofs of groups while still using the properties of B-Algebra itself.
Sensitivity Analysis of the SIRD Model for TB-Related Life Insurance Claims in Southeast Sulawesi Asni, Asriani Arsita; Fitriyani, Fitriyani; Puspita, Ira
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.36490

Abstract

Tuberculosis (TB) remains a major public health challenge in Indonesia and generates significant mortality-related risk for the life insurance sector. This study develops an integrated Susceptible–Infected–Recovered–Deceased (SIRD) model to analyze TB transmission dynamics in Southeast Sulawesi and to estimate related life insurance claims. The model is calibrated using regional TB data from 2021–2023 and validated against 2024 observations. Analytical results include equilibrium analysis and the basic reproduction number, while long-term dynamics are examined through scenario-based simulations. Epidemiological outcomes are translated into actuarial projections by converting cumulative TB-related deaths into annual incremental deaths and expected insurance claims under optimistic, baseline, and pessimistic scenarios. Parameter sensitivity is assessed using Latin Hypercube Sampling and Partial Rank Correlation Coefficients. The results show that the transmission rate is the most influential determinant of the present value of TB-related insurance claims, followed by the recovery rate, whereas TB-induced mortality has a smaller but significant effect. These findings highlight that reducing transmission and improving treatment effectiveness can simultaneously mitigate public health impacts and lower long-term insurance liabilities, demonstrating the relevance of integrating epidemiological modeling with actuarial risk assessment.
Co-Authors Fitriyani Fitriyani Muhammad Abdy Puspita, Ira Sidjara, Sahlan Wahidah Sanusi