Main Article Content


Rabies is a zoonotic disease which is spread by animals mostly carnivores. Rabies regards as tropic disease. In this article, we construct a mathematical model for rabies involving dog vaccination and dog population management. The model has two equilibrium points, namely rabies-free equilibrium point and endemic equilibrium point. We determine the effective reproduction ratio using next generation matrix. Our dynamical analysis shows that rabies-free equilibrium point is conditionally stable. A global sensitivity analysis is performed to investigate which intervention is the most crucial among the two interventions considered in the model. We use Latin hypercube sampling method to generate parameter space. To investigate the parameter sensitivity, we calculate the partial rank correlation coefficient. We provide numerical experimental results related to stability and  global sensitivity analysis. Our results show that the effective reproduction ratio is more sensitive to dog population management than vaccination intervention. This suggests that dog population management intervention, such as sterilization and monitoring of dog movements significantly reduces the effective reproduction ratio compared to vaccination programs. In addition, the number of infectious dogs has a strong correlation with dog culling actions.


rabies model global sensitivity analysis Latin hypercube sampling , partial rank correlation coefficient

Article Details


  1. [1] M. Y. Jane Ling et al., “Rabies in Southeast Asia: a systematic review of its incidence, risk factors and mortality,” BMJ Open, vol. 13, no. 5, p. e066587, May 2023, doi: 10.1136/bmjopen-2022-066587.
  2. [2] S. A. Maharani, I. L. Hilmi, and S. Salman, “Review : Efektivitas Vaksin Antirabies pada Manusia dan Cara Pemberantasan Kasus Rabies yang ada di Indonesia,” J. Ilm. Wahana Pendidik., vol. 9, no. 4, 2023, doi:
  3. [3] A. Bilal, “Rabies is a Zoonotic Disease: A Literature Review,” Occup. Med. Heal. Afffairs, vol. 9, no. 3, 2021.
  4. [4] G. Lippi and G. Cervellin, “Updates on Rabies virus disease: is evolution toward ‘Zombie virus’ a tangible threat?,” Acta Biomed., vol. 92, no. 1, 2021, doi:
  5. [5] M. J. Warrell and D. A. Warrell, “Rabies: the clinical features, management and prevention of the classic zoonosis,” Clin. Med. (Northfield. Il)., vol. 15, no. 1, pp. 78–81, Feb. 2015, doi: 10.7861/clinmedicine.14-6-78.
  6. [6] Kementerian Kesehatan RI, No Buku Saku Rabies: Petunjuk Teknis Penatalaksanaan Kasus Gigitan Hewan Penular Rabies di Indonesia. Jakarta: Kementerian Kesehatan RI, 2019.
  7. [7] ASEAN, “ASEAN Rabies Elimination Strategy,” Jakarta, 2015.
  8. [8] L. M. Smith, S. Hartmann, A. M. Munteanu, P. Dalla Villa, R. J. Quinnell, and L. M. Collins, “The Effectiveness of Dog Population Management: A Systematic Review,” Animals, vol. 9, no. 12, p. 1020, Nov. 2019, doi: 10.3390/ani9121020.
  9. [9] V. A. Astuti, “Analisis Dinamik Model Penyakit Rabies dengan Kekebalan Sementara,” Universitas Sulawesi Barat, 2022.
  10. [10] M.-M. Lv et al., “Dynamic analysis of rabies transmission and elimination in mainland China,” One Heal., vol. 17, p. 100615, Dec. 2023, doi: 10.1016/j.onehlt.2023.100615.
  11. [11] E. Ahmed, A. M. A. M. A. El-Sayed, and H. A. A. A. A. El-Saka, “Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models,” J. Math. Anal. Appl., vol. 325, no. 1, pp. 542–553, Jan. 2007, doi: 10.1016/j.jmaa.2006.01.087.
  12. [12] S. Ruan, “Modeling the transmission dynamics and control of rabies in China,” Math. Biosci., vol. 286, pp. 65–93, Apr. 2017, doi: 10.1016/j.mbs.2017.02.005.
  13. [13] A. A. Ayoade, “Integer and fractional order models for rabies: a theoretical approach,” Math. Comput. Sci., vol. 3, no. 1, 2022, doi: 10.30511/mcs.2021.541111.1046.
  14. [14] E. D. Wiraningsih et al., “Stability analysis of rabies model with vaccination effect and culling in dogs,” Appl. Math. Sci., vol. 9, pp. 3805–3817, 2015, doi: 10.12988/ams.2015.53197.
  15. [15] Fatmawati, F. F. Herdicho, Windarto, W. Chukwu, and H. Tasman, “An optimal control of malaria transmission model with mosquito seasonal factor,” Results Phys., vol. 25, p. 104238, Jun. 2021, doi: 10.1016/j.rinp.2021.104238.
  16. [16] Darmawati and W. Nur, “Stability, cost-effectiveness, and global sensitivity analysis of COVID-19 model incorporating non-pharmaceutical interventions and indirect transmission,” Data Anal. Appl. Math., vol. 3, no. 1, pp. 28–41, Mar. 2022, doi: 10.15282/daam.v3i1.7594.
  17. [17] L. K. Beay and N. Anggriani, “Dynamical Analysis of a Modified Epidemic Model with Saturated Incidence Rate and Incomplete Treatment,” Axioms, vol. 11, no. 6, 2022, doi:
  18. [18] P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Math. Biosci., vol. 180, no. 1–2, pp. 29–48, Nov. 2002, doi: 10.1016/S0025-5564(02)00108-6.
  19. [19] M. Z. Ndii, B. S. Djahi, N. D. Rumlaklak, and A. K. Supriatna, “Determining the Important Parameters of Mathematical Models of the Propagation of Malware,” in Lecture Notes in Electrical Engineering, 565th ed., Springer, 2019, pp. 1–9. doi: 10.1007/978-3-030-20717-5_1.
  20. [20] Z. Ma et al., “Modeling for COVID-19 with the contacting distance,” Nonlinear Dyn., vol. 107, no. 3, pp. 3065–3084, Feb. 2022, doi: 10.1007/s11071-021-07107-6.
  21. [21] M. S. Alam, M. Kamrujjaman, and M. S. Islam, “Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy,” J. Appl. Math. Phys., vol. 08, no. 06, pp. 941–955, 2020, doi: 10.4236/jamp.2020.86073.
  22. [22] Kementerian Kesehatan RI, “One Health Roadmap Eliminasi rabies Nasional 2030,” Jakarta, 2019.
  23. [23] E. Wera, C. Warembourg, P. M. Bulu, M. M. Siko, and S. Dürr, “Immune Response After Rabies Vaccination in Owned Free-Roaming Domestic Dogs in Flores Island, Indonesia,” Front. Vet. Sci., vol. 9, Jun. 2022, doi: 10.3389/fvets.2022.868380.
  24. [24] D. L. Knobel, T. Lembo, M. Morters, S. E. Townsend, S. Cleaveland, and K. Hampson, “Dog Rabies and Its Control,” in Rabies, Third., Elsevier, 2013, pp. 591–615. doi: 10.1016/B978-0-12-396547-9.00017-1.
  25. [25] R. S. Pratiwi and G. K. Wadrianto, “Berapa Lama Usia Hidup Anjing? Ini Penjelasannya,” 2021. (accessed Oct. 20, 2023).
  26. [26] Centers for Disease Control and Prevention, “Rabies,” 2022. (accessed Oct. 20, 2023).