Sensitivity Analysis of the SIRD Model for TB-Related Life Insurance Claims in Southeast Sulawesi

Asriani Arsita Asni, Fitriyani Fitriyani, Ira Puspita

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.

Keywords


Life Insurance Claims; Numerical Simulation; Sensitivity Analysis; SIRD Model; Tuberculosis.

Full Text:

PDF

References


[1] Sesar Dayu Pralambang and Sona Setiawan. “Faktor Risiko Kejadian Tuberkulosis di Indonesia”. In: Jurnal Biostatistik, Kependudukan, dan Informatika Kesehatan 2.1 (2021), pp. 60–71. doi: 10.7454/bikfokes.v2i1.1023.

[2] WHO. Global Tuberculosis Report 2023. Geneva: World Health Organization, 2024. https://iris.who.int/bitstream/handle/10665/373828/9789240083851-eng.pdf.

[3] Kemenkes. Menkes Tegaskan Indonesia Serius Tangani TBC. 2024. https://kemkes.go.id/id/menkes-tegaskan-indonesia-serius-tangani-tbc (visited on 08/25/2025).

[4] Hariati Lestari. “Analisis Epidemiologi Kejadian Tuberkulosis di Provinsi Sulawesi Tenggara Tahun 2021–2023”. In: Variable Research Journal 1.2 (2024), pp. 802–810. https://variablejournal.my.id/index.php/VRJ/article/view/116.

[5] Danik Iga Prasiska, Durga Datta Chapagain, et al. “Non-communicable Comorbidities in Pulmonary Tuberculosis and Healthcare Utilization: A Cross-sectional Study of 2021 Indonesian National Health Insurance Data”. In: Archives of Public Health 82.127 (2024). doi: 10.1186/s13690-024-01352-y.

[6] Aldi Eka Wahyu Widanto, Julinar Julinar, and Venansius Ryan Tjahjono. “Penentuan Effective Reproduction Number COVID-19 dengan Metode Particle Swarm Optimization pada Enam Provinsi di Pulau Jawa.” In: Limits: Journal of Mathematics and Its Applications 20.2 (2023). doi: 10.12962/limits.v20i2.8585.

[7] Devosmita Sen and Debasis Sen. “Use of a Modified SIRD Model to Analyze COVID-19 Data”. In: Industrial & Engineering Chemistry Research 60.11 (2021), pp. 4251–4260. doi: 10.1021/acs.iecr.0c04754.

[8] Simeon Adeyemo, Adekunle Sangotola, and Olga Korosteleva. “Modeling Transmission Dynamics of Tuberculosis–HIV Co-Infection in South Africa”. In: Epidemiologia 4.4 (2023), pp. 408–419. doi: 10.3390/epidemiologia4040036. https://www.mdpi.com/2673-3986/4/4/36.

[9] P. H. P. Cintra, M. F. Citeli, and F. N. Fontinele. Mathematical Models for Describing and Predicting the COVID-19 Pandemic Crisis. 2020. https://arxiv.org/abs/2006.02507.

[10] Merry Adelindra and Vina Lusiana. “Model Matematika SEIT untuk Penyebaran Penyakit Diabetes Non Genetik”. In: Jurnal P4I 4.4 (2024), pp. 161–172. doi: 10.51878/knowledge.v4i4.3942.

[11] Darsih Idayani, Asmara Iriani Tarigan, et al. “Model Matematika SVEIAR Penularan Covid-19 di Indonesia dengan Intervensi Vaksinasi dan Tradisi Mudik”. In: Euler: Jurnal Ilmiah Matematika, Sains dan Teknologi 13.1 (2025), pp. 21–29. doi: 10.37905/euler.v13i1.30231.

[12] Purnami Widyaningsih, William Kristianto, and Dewi Retno Sari Saputra. “Model Susceptible Vaccinated Infected Recovered: Formulasi dan Penerapan Model pada Penyebaran Penyakit Campak di Indonesia”. In: Aksioma: Jurnal Matematika dan Pendidikan Matematika 12.2 (2024), pp. 271–278. https://journal.upgris.ac.id/index.php/aksioma/article/view/9271.

[13] Bo Yang, Zhenhua Yu, and Yuanli Cai. “The Impact of Vaccination on the Spread of COVID-19: Studying by a Mathematical Mode”. In: Physica A: Statistical Mechanics and Its Applications 490 (2022). doi: h10.1016/j.physa.2021.126717.

[14] Abdul Malek and Ashabul Hoque. “Mathematical Model of Tuberculosis with Seasonality, Detection, and Treatment”. In: Informatics in Medicine Unlocked 49 (2024). doi: 10.1016/j.imu.2024.101536.

[15] Muhammad Ahsar Karim and Yuni Yulida. “Analisis Kestabilan dan Sensitivitas pada Model Matematika SEIRD dari Penyebaran Covid-19: Studi Kasus di Kalimantan Selatan”. In: Media Bina Ilmiah 16.5 (2021), pp. 7003–7012. https://repo-dosen.ulm.ac.id/handle/123456789/22582.

[16] Arista Fitri Diana, Muhammad Ibnu Hajar, et al. “Analisis Kestabilan Lokal Model Transmisi Demam Berdarah Dengue”. In: Square: Journal of Mathematics and Mathematics Education 6.1 (2024), pp. 41–54. doi: 10.21580/square.2024.6.1.21018.

[17] Saumen Barua and Attila Dénes. “Global Dynamics of a Compartmental Model to Assess the Effect of Transmission from Deceased”. In: Mathematical Biosciences 364 (2023). doi: 10.1016/j.mbs.2023.109059.

[18] Gesti Essa Waldani. “Hopf Bifurcation in a Dynamic Mathematical Model in Facultative Waste Stabilization Pond”. In: Jurnal Matematika, Statistika dan Komputasi 21.2 (202), pp. 544–559. doi: 10.20956/j.v21i2.41888.

[19] Merry Adelindra and Vina Lusiana. “Stability Analysis of Mathematical Models of Toxoplasmosis Spread in Cat and Human Populations with Time Delay”. In: Formosa Journal of Science and Technology 2.2 (2023), pp. 443–452. doi: 10.55927/fjst.v2i2.2855.

[20] Wiwik Tri Hardianti. “Analisis Sensitivitas Model Epidemik SEIR pada Penyebaran Penyakit dengan Karantina”. In: Innovative: Journal Of Social Science Research 4.6 (2024), pp. 3134–3143. doi: 10.31004/innovative.v4i6.16516.

[21] J Harianto and KL Tuturop. “Analisis Sensitivitas Model Matematika Penyebaran Penyakit Tuberkulosis”. In: Jurnal Ilmiah Matematika dan Terapan 19.1 (2022), pp. 29–38. doi: 10.22487/2540766X.2022.v19.i1.15802.

[22] Sara Soulaimani, Abdelilah Kaddar, and Fathalla A. Rihan. “Stochastic Stability and Global Dynamics of a Mathematical Model for Drug Use: Statistical Sensitivity Analysis Via PRCC”. In: Partial Differential Equations in Applied Mathematics 12 (2024). doi: 10.1016/j.padiff.2024.100964.

[23] Zulfatin Nafizah and Yudi Ari Adi. “Model SEIR dengan Pseudo-recovery pada Kasus Tuberkulosis di Jawa Barat”. In: Jurnal Matematika UNAND 13.3 (2024), pp. 170–187. doi: 10.25077/jmua.13.3.170-187.2024.

[24] Eka Riztina Zega and Zahri Fdli. “Analisis Sistem dan Prosedur Penyelesaian Klaim Asuransi Jiwa pada Ajb Bumiputera 1912”. In: Innovative: Journal Of Social Science Research 3.5 (2023), pp. 9941–9955. https://j-innovative.org/index.php/Innovative/article/view/5819.

[25] Ellen Putri Manggarini. “Analisis Rasio Risk-Based Capital sebagai Prediksi Financial Distress pada Perusahaan Asuransi Jiwa di Indonesia”. In: Jurnal Manajerial Bisnis 6.2 (2023), pp. 109–124. doi: 10.37504/jmb.v6i2.495.

[26] Andri Afrianto, Tony Irawan, and Alla Asmara. “Pandemi Covid-19 dan Dampaknya Terhadap Klaim Asuransi di Indonesia: Studi Kasus BPJS Ketenagakerjaan”. In: Jurnal Aplikasi Bisnis dan Manajemen 9.3 (2023), pp. 908–918. doi: 10.17358/jabm.9.3.908.

[27] Jonathan Hoseana, Felivia Kusnad, et al. “Design and Financial Analysis of a Health Insurance Based on an SIH-Type Epidemic Model”. In: Journal of Mathematics and Computer Science 38.2 (2024), pp. 1–20. doi: 10.48550/arXiv.2408.05397.

[28] HainautDonatien. “An Actuarial Approach for Modeling Pandemic Risk”. In: Journal of Mathematics and Computer Science 9.3 (2020). doi: 10.3390/risks9010003.

[29] Chang Zhai et al. “Epidemic Modelling and Actuarial Applications for Pandemic Insurance: A Case Study of Victoria, Australia”. In: Annals of Actuarial Science 18.2 (2024), pp. 242–269. doi: 10.1017/S1748499523000246.

[30] Asni Arsita, Ilham Minggi, et al. “Deciphering Celebrity Worship Phenomenon: Simulation and Analysis using SFR Mathematical Model with Time Delay among Fans in South Sulawesi”. In: Journal of Mathematics, Computations, and Statistics 7.1 (2024), pp. 173–184. doi: 10.35580/jmathcos.v7i1.4251.

[31] Asriani Arsita Asni, Ilham Minggi, et al. “Mathematical Model of Celebrity Worship Tendency Among K-Pop Fans in South Sulawesi”. In: ITM Web of Conferences 58.01004 (2024). doi: 10.1051/itmconf/20245801004.

[32] Sebi Khatun, Palakshi Paul, and Pritha Das. “Exploring Cost-Effectiveness Analysis in Delayed Optimal Control and Complex Dynamics of an Epidemic Model with Media Coverage”. In: Communications in Nonlinear Science and Numerical Simulation 152 (2025). doi: 10.1016/j.cnsns.2025.109109.

[33] Dipo Aldila. “Change in Stability Direction Induced by Temporal Interventions: A Case Study of a Tuberculosis Transmission Model with Relapse and Reinfection”. In: Frontiers in Applied Mathematics and Statistics 11 (2025). doi: 10.3389/fams.2025.1541981.

[34] Siying Xiong et al. “Estimation Methods of Reproduction Numbers for Epidemics of Varying Strains of COVID-19”. In: Journal of Biosafety and Biosecurity 6.4 (2024), pp. 265–270. doi: 10.1016/j.jobb.2024.10.003.

[35] Haileyesus Tessema Alemneh and Negesse Yizengaw Alemu. “Mathematical Modeling with Optimal Control Analysis of Social Media Addiction”. In: Infectious Disease Modelling 6 (2021), pp. 405–419. doi: 10.1016/j.idm.2021.01.011.

[36] Fatmawati et al. “The Dynamics Of Tuberculosis Transmission With Optimal Control Analysis In Indonesia”. In: Communications in Mathematical Biology and Neuroscience 2020.25 (2020). doi: 10.28919/cmbn/4605.

[37] F. J. Cuesta-Valero et al. “A New Bootstrap Technique to Quantify Uncertainty in Estimates of Ground Surface Temperature and Ground Heat Flux Histories from Geothermal Data”. In: Geoscientific Model Development 15.20 (2022), pp. 7913–7932. doi: 10.5194/gmd-15-7913-2022.

[38] P. Dutilleul, C. Genest, and R. Peng. “Bootstrapping for Parameter Uncertainty in the Space–Time Epidemic-Type Aftershock Sequence Model”. In: Geophysical Journal International 236.3 (2024), pp. 1601–1608. doi: 10.1093/gji/ggae003.

[39] T. O. Hodson. “Root-Mean-Square Error (RMSE) or Mean Absolute Error (MAE): When to Use Them or Not”. In: Geoscientific Model Development 15.14 (2022), pp. 5481–5487. doi: 10.5194/gmd-15-5481-2022.

[40] Donatien Hainaut. “An Actuarial Approach for Modeling Pandemic Risk”. In: Risks 9.1 (2021). doi: 10.3390/risks9010003.

[41] Runhuan Feng, Longhao Jin, and Sooie-Hoe Loke. “Interplay between Epidemiology and Actuarial Modeling”. In: Casualty Actuarial Society E-Forum (2021). https://www.casact.org/sites/default/files/2021-05/Feng_et_al_Epidemiology_and_Actuarial_Modeling.pdf.

[42] Chang Zhai et al. “Epidemic Modelling and Actuarial Applications for Pandemic Insurance: A Case Study of Victoria, Australia”. In: Annals of Actuarial Science 18.2 (2024), pp. 242–269. doi: 10.1017/S1748499523000246.




DOI: https://doi.org/10.18860/cauchy.v11i1.36490

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Asriani Arsita Asni, Fitriyani Fitriyani, Ira Puspita

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.