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Abstract
Rabies is a fatal zoonotic disease that is generally transmitted through the bite of an infected dog. This research aims to predict the spread of rabies in dog and human populations in Muara Enim Regency using a combined SI–SEIR mathematical model. The system of nonlinear differential equations was solved using the fourth-order Runge–Kutta (RK4) method. Rabies data on dogs and humans were obtained from the Lampung Veterinary Center for the period 2021–2024. The simulation results show that the number of infected dogs increased significantly at the beginning of the period, peaked in the third year, and then declined as the population of susceptible dogs decreased. In the human population, the increase in exposed and infected individuals occurred after the surge in the dog population, indicating cross-species transmission. This model provides a quantitative overview of rabies dynamics and can be used as a basis for rabies control strategies in Muara Enim Regency.
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References
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References
K. Hampson, L. Coudeville, T. Lembo, M. Sambo, A. Kieffer, M. Attlan, J. Barrat, J. D. Blanton, D. J. Briggs, S. Cleaveland, et al., “Estimating the global burden of endemic canine rabies,” PLoS neglected tropical diseases, vol. 9, no. 4, p. e0003709, 2015. https://doi.org/10.1371/journal.pntd.0003709.
World Health Organisation, “Rabies,” 2022. https://www.who.int/news-room/fact-sheets/detail/rabies.
Kementerian Kesehatan Republik Indonesia, “Profil kesehatan indonesia,” 2023. http://kemkes.go.id/app_asset/file_content_download/172231123666a86244b83fd8.51637104.pdf.
H. Younas, I. Ahmad, N. Ali, I. U. Haq, M. D. Albalwi, S. Muhammad, and M. Shuaib, “Modeling rabies dynamics: the impact of vaccination and infectious immigrants on public health,” Contemporary Mathematics, pp. 3255–3279, 2024. https://doi.org/10.37256/cm.5320245010.
N. Mahwayi, A mathematical model assessing the impact of rabies on human and stray dogs. University of Johannesburg (South Africa), 2024. https://hdl.handle.net/10210/516567.
P. A. Naik, B. Murthy, M. Srinivas, L. Chada, M. N. Raju, and D. Saradhi, “Exploring the dynamics of rabies epidemic model using caputo-fabrizio derivative under treatment and vaccination,” Computer Methods in Biomechanics and Biomedical Engineering, pp. 1–19, 2026. https://doi.org/10.1080/10255842.2026.2613116.
J. A. Tolentino, J. Alonte, P. Benalla, E. R. A. Jamito, M. A. Salvador, and R. Villanueva, “Dynamics of rabies spread using mathematical modeling and simulation,” Kafrelsheikh Journal of Information Sciences, vol. 5, no. 2, 2025. https://vixra.org/abs/2411.0121.
N. Chitnis, “Introduction to seir models,” in Workshop on mathematical models of climate variability, environmental change and infectious diseases, Trieste, Italy, 2017. https://indico.ictp.it/event/7960/session/3/contribution/19/material/slides/0.pdf.
M. Charles, V. G. Masanja, D. F. Torres, S. G. Mfinanga, and G. Lyakurwa, “Mathematical model to assess the impact of contact rate and environment factor on transmission dynamics of rabies in humans and dogs,” Heliyon, vol. 10, no. 11, 2024. https://doi.org/10.1016/j.heliyon.2024.e32012.
E. D. Wiraningsih, W. Aryati, S. Toaha, and S. Lenhart, “Optimal control for seir rabies model between dogs and human with vaccination effect in dogs,” in Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010), vol. 6, pp. 161–1175, Universiti Tunku Abdul Rahman Kuala Lumpur, Malaysia, 2010. https://shorturl.at/YEsdF.
D. Dejene and P. R. Koya, “Population dynamics of dogs subjected to rabies disease,” InterOSR Journal of Mathematics (IOSR-JM), vol. 12, no. 3, pp. 2319–2765, 2016. https://doi.org/10.9790/5728-120304110120
M. R. A. Nurdiansyah, S. Toaha, et al., “Stability analysis and numerical simulation of rabies spread model with delay effects,” AIMS Mathematics, vol. 9, no. 2, pp. 3399–3425, 2024. https://www.aimspress.com/article/doi/10.3934/math.2024167.
G. Arora, V. Joshi, and I. S. Garki, “Developments in runge–kutta method to solve ordinary differential equations,” in Recent Advances in Mathematics for Engineering, pp. 193–202, CRC Press, 2020. https://doi.org/10.1201/9780429200304-9.
A. Papalia, Y. A. Lesnussa, M. E. Rijoly, and O. J. Peter, “Numerical solution of the seir model using the fourth-order runge-kutta method to predict the spread of hepatitis b disease in ambon city,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 18, no. 3, pp. 2047–2056, 2024. https://doi.org/10.30598/barekengvol18iss3pp2047-2056.
N. T. Sapulette, Y. A. Lesnussa, and M. E. Rijoly, “Numerical solution of the sirv model using the fourth-order runge-kutta method,” Jurnal Matematika Vol, vol. 13, no. 2, pp. 105–115, 2023. https://doi.org/10.24843/JMAT.2023.v13.i02.p164.
N. D. Harvey, “How old is my dog? identification of rational age groupings in pet dogs based upon normative age-linked processes,” Frontiers in Veterinary Science, vol. 8, p. 643085, 2021. https://doi.org/10.3389/fvets.2021.643085.
L. Wu, Y. Zhang, Z. Huang, H. Lu, X. Li, Q. Zhu, C. Yin, J. Liu, H. Shao, and X. Sun, “Antibody persistence of human diploid cell rabies vaccine administrated using the four-versus five-dose essen intramuscular regimen in post-exposure prophylaxis: A prospective cohort study among the chinese population,” Vaccines, vol. 13, no. 3, p. 215, 2025. https://doi.org/10.3390/vaccines13030215?urlappend=%3Futm_source%3Dresearchgate.net%26utm_medium%3Darticle.