Trends in Immunotherapy

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Comparative Analysis of Classical and Fractional-Order Models for Rabies Transmission

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https://doi.org/10.54963/ti.v9i3.1346
Jothi, N. K., Muruganandham, A., Deepa. S, Abraham, N. A., & Mattuvarkuzhali, C. (2025). Comparative Analysis of Classical and Fractional-Order Models for Rabies Transmission. Trends in Immunotherapy, 9(3), 110–139. https://doi.org/10.54963/ti.v9i3.1346
Volume 9 Issue 3 (2025)
Copyright (c) 2025 Naresh Kumar Jothi, Anusha Muruganandham, Deepa. S, Neel Armstrong Abraham, Chandrasekaran Mattuvarkuzhali
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Authors

  • Naresh Kumar Jothi

    Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu 600062, India
  • Anusha Muruganandham

    Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu 600062, India
  • Deepa. S

    Department of Mathematics, Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Chennai, Tamil Nadu 600062, India
  • Neel Armstrong Abraham

    Department of Mathematics, PaniMalar Engineering College, Poonamallee, Chennai, Tamil Nadu 600123, India
  • Chandrasekaran Mattuvarkuzhali

    Department of Mathematics, Vel Tech Multi Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Chennai, Tamil Nadu 600062, India

Received: 24 June 2025; Revised: 1 July 2025; Accepted: 7 July 2025; Published: 6 August 2025

Rabies is still a serious public health problem globally, especially where there is high dog-to-human contact and low vaccination coverage. In this paper, a fractional-order mathematical model is developed to explain the transmission dynamics of rabies in dogs and humans. The model is established by adopting the Caputo-Fabrizio fractional-order derivative (CFFROD), which suits the memory effects and non-locality properties of disease progression. The model has compartments for susceptible, exposed, infected, and recovered members of both species, as well as the viral load in the environment. Existence and uniqueness of solutions are proven via fixed-point theory to ensure mathematical consistency of the model. Numerical computations via the Adams-Bashforth method are performed to analyse the dynamics of the system for a range of fractional orders. Numerical computations provide evidence that fractional-order dynamics have a considerable impact on disease progression, ensuring the significance of memory in infectious disease modelling. Based on verified experimental data, a comparison between the fractional-order and classical models is presented. The results show that the fractional model provides greater insight into transmission and control timing patterns and best fits real-world data. This study supports the use of fractional modelling in the well-informed creation of successful rabies prevention initiatives and improved comprehension of disease dynamics.

Keywords:

Rabies Transmission Fractional Order Derivative (FROD) Caputo-Fabrizio Fractional Derivative (CFFROD) Disease Dynamics Fixed Point Theory Numerical Simulation Adams-Bashforth Method Susceptible-Exposed-Infected-Recovered (SEIR) Model

References

  1. Peter, O.J.; Shaikh, A.S.; Ibrahim, M.O.; et al. Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator. Comput. Mater. Contin. 2021, 66, 1823–1848.
  2. Ullah, S.; Khan, M.A.; Farooq, M.; et al. A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative. Discrete Contin. Dyn. Syst. Ser. S 2020, 13, 975–993.
  3. Nisar, K.S.; Farman, M.; Abdel-Aty, M.; et al. A Review on Epidemic Models in Sight of Fractional Calculus. Alex. Eng. J. 2023, 75, 81–113.
  4. Khan, T.; Ullah, R.; Zaman, G.; et al. A Mathematical Model for the Dynamics of SARS-CoV-2 Virus Using the Caputo-Fabrizio Operator. Math. Biosci. Eng. 2021, 18, 6095–6116.
  5. Alzahrani, E.; El-Dessoky, M.M.; Baleanu, D. Modelling the Dynamics of the Novel Coronavirus Using Caputo-Fabrizio Derivative. Alex. Eng. J. 2021, 60, 4651–4662.
  6. Rezapour, S.; Etemad, S.; Mohammad, H. A Mathematical Analysis of a System of Caputo–Fabrizio Fractional Differential Equations for the Anthrax Disease Model in Animals. Adv. Contin. Discrete Models 2020, 481, 1–30.
  7. Zhang, X.H.; Ali, A.; Khan, M.A.; et al. Mathematical Analysis of the TB Model with Treatment via Caputo-Type Fractional Derivative. Discrete Dyn. Nat. Soc. 2021, 2021, 1–15.
  8. Jothi, N.K.; Vadivelu, V.; Dayalan, S.K.; et al. Dynamic Interactions of HSV-2 and HIV/AIDS: A Mathematical Modeling Approach. AIP Adv. 2024, 14, 1–16.
  9. Rahman, M.U.; Karaca, Y.; Agarwale, R.P.; et al. Mathematical Modelling with Computational Fractional Order for the Unfolding Dynamics of the Communicable Diseases. Appl. Math. Sci. Eng. 2024, 32, 1–34.
  10. Adnan; Ali, A.; Rahman, M.U.; et al. Investigation of Time-Fractional SIQR COVID-19 Mathematical Model with Fractal-Fractional Mittage-Leffler Kernel. Alex. Eng. J. 2022, 61, 7771–7779.
  11. Jothi, N.K.; Rasappan, S. Stabilization and Complexities of Anopheles Mosquito Dynamics with Stochastic Perturbations. IAENG Int. J. Appl. Math. 2017, 47, 307–311.
  12. Hamou, A.A.; Azroul, E.; Alaoui, A.L. Fractional Model and Numerical Algorithms for Predicting COVID-19 with Isolation and Quarantine Strategies. Int. J. Appl. Comput. Math. 2021, 7, 142–172.
  13. Liu, X.; Ullah, S.; Alshehri, A.; et al. Mathematical Assessment of the Dynamics of Novel Coronavirus Infection with Treatment: A Fractional Study. Chaos Solitons Fractals 2021, 153, 1–19.
  14. Tuan, N.H.; Mohammadi, H.; Rezapour, S. A Mathematical Model for COVID-19 Transmission by Using the Caputo Fractional Derivative. Chaos Solitons Fractals 2020, 140, 1–11.
  15. Askar, S.S.; Ghosh, D.; Santra, P.K.; et al. A Fractional Order SITR Mathematical Model for Forecasting of Transmission of COVID-19 of India with Lockdown Effect. Results Phys. 2021, 24, 1–11.
  16. Ahmad, S.; Ullah, A.; Al-Mdallal, Q.M.; et al. Fractional Order Mathematical Modelling of COVID-19 Transmission. Chaos Solitons Fractals 2020, 139, 1–10.
  17. Jothi, N.K.; Suresh, M.L.; Mai, T.N.M.M. Mathematical Model for the Control of Life Cycle of Feminine Anopheles Mosquitoes. Int. J. Recent Technol. Eng. 2019, 8, 5316–5319.
  18. Chakraborty, S.; Paul, J.; Deshmukh, R. Emerging Therapies for Rabies: Combining Antiviral and Antioxidant Strategies. Curr. Opin. Virol. 2022, 52, 18–24.
  19. World Health Organization. Rabies Vaccines: WHO Position Paper, 2023; WHO: Geneva, Switzerland, 2023.
  20. Centers for Disease Control and Prevention (CDC). Rabies Treatment and Prophylaxis Guidelines; CDC: Atlanta, GA, USA, 2024.
  21. Dutta, S.; Mukherjee, D. A Review of Global Rabies Control Strategies and Their Integration with Clinical Treatments. Glob. Health Rev. 2023, 9, 101–109.
  22. Peter, O.J.; Yusuf, A.; Ojo, M.M.; et al. A Mathematical Model Analysis of Meningitis with Treatment and Vaccination in Fractional Derivatives. Int. J. Appl. Comput. Math. 2022, 117, 1–28.
  23. Yusuf, A.; Acay, B.; Mustapha, U.T.; et al. Mathematical Modelling of Pine Wilt Disease with Caputo Fractional Operator. Chaos Solitons Fractals 2021, 143, 1–13.
  24. Prathumwan, D.; Chaiya, I.; Trachoo, K. Study of Transmission Dynamics of Streptococcus suis Infection Mathematical Model Between Pig and Human Under ABC Fractional Order Derivative. Symmetry 2022, 14, 1–21.
  25. Jothi, N.K.; Muruganandham, A.; Krithika, S.; et al. Analysis and Control of the Caputo Fractional-Order Model for the Transmission of the Rabies Virus. Afr. J. Biomed. Res. 2024, 27, 67–78.
  26. Chatterjee, A.N.; Al Basir, F.; Ahmad, B.; et al. A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor. Mathematics 2022, 10, 1–15.
  27. Liu, B.; Farid, S.; Ullah, S.; et al. Mathematical Assessment of Monkeypox Disease with the Impact of Vaccination Using a Fractional Epidemiological Modelling Approach. Sci. Rep. 2023, 13, 1–27.
  28. El Hadj Moussa, Y.; Boudaoui, A.; Ullah, S.; et al. Stability Analysis and Simulation of the Novel Coronavirus Mathematical Model via the Caputo Fractional-Order Derivative: A Case Study of Algeria. Results Phys. 2021, 26, 1–14.
  29. Jothi, N.K.; Muruganandham, A.; Stalin, T.; et al. Ecological Dynamics and Control Strategies of the Feminine Anopheles stephensi Using Volterra Lyapunov Function. J. Orient. Inst. 2023, 72, 117–127.
  30. Alazman, I.; Alkahtani, B.S.T. Investigation of Novel Piecewise Fractional Mathematical Model for COVID-19. Fractals Fract. 2022, 6(11), 1–26.
  31. Jothi, N.K.; Lakshmi, A. Development and Analysis of Malaria Vector by Mathematical Modelling. In Emergent Converging Technologies and Biomedical Systems, Jain, S., Marriwala, N., Singh, P., et al., Eds.; Springer: Singapore, 2024; pp. 551–562.
  32. Hailemichael, D.D.; Edessa, G.K.; Koya, P.R. Mathematical Modelling of Dog Rabies Transmission Dynamics Using Optimal Control Analysis. Contemp. Math. 2023, 4, 296–319.
  33. Odibat, Z.M.; Shawagfeh, N.T. Generalized Taylor’s Formula. Appl. Math. Comput. 2007, 186, 286–293.
  34. Jothi, N.K.; Muruganandham, A.; Kumar, P.S.; et al. Modeling Rabies Transmission Dynamics with Fractional Order Analysis: Examining Stability, Susceptibility, and Vaccination Impact. AIP Adv. 2025, 15(5), 055116.
  35. Kaur, M.; Sharma, A.; Gupta, R.K. Modified Antioxidants in Adjunctive Rabies Therapy: A Review of Recent Developments. J. Trop. Med. Infect. Dis. 2023, 12, 245–253.
  36. Smith, L.; Oliveira, R.; Hossain, M. Novel Monoclonal Antibody Therapies in the Management of Rabies. Infect. Dis. Rep. 2023, 15, 55–63.