Mathematical analysis of unreported gender based sexual violence cases in Indonesia
Abqorry Zakiyyahabqorryz@gmail.comDepartment of Mathematics and Data Science, Faculty of Mathematics and Natural ScienceAndalas UniversityPadang, 25163, IndonesiaView full profile → , *Susila BahriCorresponding authorsusilabahri@sci.unand.ac.idDepartment of Mathematics and Data ScienceFaculty of Mathematics and Natural ScienceAndalas UniversityPadang 25163, IndonesiaView full profile → , Arrival Rince Putriarrival@sci.unand.ac.idDepartment of Mathematics and Data ScienceFaculty of Mathematics and Natural ScienceAndalas UniversityPadang 25163, IndonesiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jul 2025
- Published Online:
- 31 Jul 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2428
- Pages:
- 2249–2261
Abstract
Sexual violence remains a pervasive public health and social issue, with the World Health Organization reporting that one in three women globally experiences such violence in their lifetime. Moreover, more than half of the victims do not report their experiences, underscoring the need for analytical tools that account for both reported and unreported cases. This study presents a nonlinear compartmental model (SUVPR: Susceptible–Unreported Violence–Reported Violence–Punishment–Recovered) to analyze the underlying mechanisms and contributing factors that shape the dynamics of gender based sexual violence in Indonesia. The model incorporates key behavioural and reporting dynamics to reflect real-world conditions accurately. Using the next-generation matrix method, we derive the basic reproduction numbers R_0=0.0117309 for the sexual violence-free equilibrium point and R_0=1.10671391 for the sexual violence endemic equilibrium point. The analysis with the Routh-Hurwitz criterion indicates that both equilibrium points are locally asymptotically stable under certain parameter conditions. The identification of the effective contact rate and the reporting rate as key determinants of R_0 indicates that enhancing reporting mechanisms and reducing societal tolerance toward violence may substantially mitigate the transmission dynamics of sexual violence.
Keywords
Subject Classifications
References
[1] World Health Organization, “Violence information,” (2024). [Online]. Available: https://apps.who.int/violence-info/sexual-violence/. [Accessed: May 8, 2025].
[2] V. A. Women, “Prevalence estimates, 2018,” Americas, vol. 25, p. 7 (2021).
[3] K. Perempuan, “CATAHU 2023: Peluang penguatan sistem penyikapan di tengah peningkatan kompleksitas kekerasan terhadap perempuan,” (2023). [Online]. Available: https://komnasperempuan.go.id/catatan-tahunan-detail/catahu-2023-peluang-penguatan-sistem-penyikapan-di-tengah-peningkatan-kompleksitas-kekerasan-terhadap-perempuan.
[4] K. Perempuan and R. Eksekutif, “Menata data, menajamkan arah: Refleksi pendokumentasian dan tren kasus kekerasan terhadap perempuan 2024,” Catatan Tahunan Kekerasan Terhadap Perempuan Tahun, p. 7 (2024).
[5] E. M. A. Stephanie, L. G. B. Ruiz, M. A. Vila, and M. C. Pegalajar, “Study of violence against women and its characteristics through the application of text mining techniques,” Int. J. Data Sci. Anal., vol. 18, no. 1, pp. 35–48 (2024).
[6] F. Carrillo-Brenes, L. M. Vilches-Blázquez, and S. D. Orantes-Jiménez, “Spatial regression models on sexual violence against women in Mexico City,” in GIS LATAM Conf., Cham, Switzerland: Springer Nature Switzerland, pp. 105–121 (Sep. 2024).
[7] S. Bahri, H. R. Riyandi, and B. Rudianto, “Stability of the dynamic model of SVPR sexual violence cases,” BAREKENG: J. Ilmu Mat. dan Terap., vol. 18, no. 3, pp. 1719–1728 (2024).
[8] T. P. INFID, Laporan Studi Kuantitatif Barometer Kesetaraan Gender. Jakarta, Indonesia: INFID (2020).
[9] G. T. Tilahun and H. T. Alemneh, “Mathematical modeling and optimal control analysis of COVID-19 in Ethiopia,” J. Interdiscip. Math., vol. 24, no. 8, pp. 2101–2120 (2021).
[10] J. O. Agbomola and A. C. Loyinmi, “Modelling the impact of some control strategies on the transmission dynamics of Ebola virus in human-bat population: An optimal control analysis,” Heliyon, vol. 8, no. 12 (2022).
[11] G. Simorangkir, D. Aldila, A. Rizka, H. Tasman, and E. S. Nugraha, “Mathematical model of tuberculosis considering observed treatment and vaccination interventions,” J. Interdiscip. Math., vol. 24, no. 6, pp. 1717–1737 (2021).
[12] S. Bahri, A. Mardiyah, A. I. Baqi, and A. Zakiyyah, “Local stability analysis and simulation of omicron virus spread using the omicron SSvIR model,” IAENG Int. J. Appl. Math., vol. 54, no. 5, pp. 797–803 (2024).
[13] P. L. Delamater, E. J. Street, T. F. Leslie, Y. T. Yang, and K. H. Jacobsen, “Complexity of the basic reproduction number (R0),” Emerg. Infect. Dis., vol. 25, no. 1, p. 1 (2019).
[14] S. Bahri, I. Fitrialita, H. Nasution, R. Lestari, and L. Fajria, “Analysis of the effects of foreign travelers and immigrants on omicron transmission in Indonesia,” Int. J. Math. Comput. Sci., vol. 19, no. 3, pp. 893–902 (2024).
[15] P. B. Borah, K. Dehingia, H. K. Sarmah, and H. Emadifar, “Dynamics of simultaneous propagation of two COVID-19 strains,” Adv. Contin. Discrete Models, vol. 2025, no. 1, p. 45 (2025).
[16] D. N. Fisman, A. L. Greer, and A. R. Tuite, “Bidirectional impact of imperfect mask use on reproduction number of COVID-19: A next generation matrix approach,” Infect. Dis. Model., vol. 5, pp. 405–408 (2020).
[17] W. Hao, J. Zhang, Z. Peng, and Z. Jin, “Evaluating the current status and strategies of achieving the 95-95-95 target for HIV/AIDS: A mathematical model,” Discrete Contin. Dyn. Syst. B, vol. 30, pp. 3829-3857 (2025).
[18] S. D. Fisher, Complex Variables. Mineola, USA: Courier Corporation (1999).
[19] K. Trachoo, I. Chaiya, and D. Prathumwan, “An improved mathematical modeling of bone remodeling: The role of stability in predicting bone health,” Adv. Contin. Discrete Models, vol. 2025, no. 1, p. 73 (2025).
[20] S. Bahri, A. R. Rahmanda, H. Haripamyu, I. M. Arnawa, A. Zakiyyah, and H. Yetti, “Epidemiological dynamics of measles transmission with incomplete vaccination: Evidence from Indonesia,” Int. J. Math. Comput. Sci., vol. 21, no. 1, pp. 221–226 (2026).
