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A Caputo Fractional‐Order Model for Dog Rabies Transmission With Vaccination: A Case Study of Ulanga District, Tanzania

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  • Jufren Zakayo Ndendya
  • Stephen Edward
  • Maganga Sambo

Abstract

Dog rabies remains a major public health concern in many regions, including Ulanga District, Morogoro, Tanzania. This study develops a fractional‐order compartmental model employing Caputo derivatives to incorporate memory effects, providing a more realistic representation of rabies transmission dynamics. We establish the positivity and boundedness of solutions, and prove the existence of both disease‐free equilibrium (DFE) and endemic equilibrium (EE) points. The basic reproduction number, Re, is derived using a graph‐theoretic approach and characterizes the system’s global stability: the DFE is locally stable when Re 1. Hyers–Ulam stability analysis confirms the model’s robustness under small perturbations, reinforcing the validity of the fractional‐order framework. The model is calibrated using Bayesian Markov Chain Monte Carlo (MCMC) techniques with field data. Numerical simulations indicate that strong memory effects (i.e., lower values of the fractional order ϕ) significantly reduce infection levels in dog populations and influence the long‐term behavior of the vaccinated class. Further simulations under varying vaccination coverage levels show a substantial decline in the susceptible population, while also revealing the necessity for complementary control measures to effectively reduce the infections.

Suggested Citation

  • Jufren Zakayo Ndendya & Stephen Edward & Maganga Sambo, 2025. "A Caputo Fractional‐Order Model for Dog Rabies Transmission With Vaccination: A Case Study of Ulanga District, Tanzania," Abstract and Applied Analysis, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnlaaa:v:2025:y:2025:i:1:n:6679795
    DOI: 10.1155/aaa/6679795
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    References listed on IDEAS

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    1. Din, Anwarud & Li, Yongjin & Khan, Tahir & Zaman, Gul, 2020. "Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Joshua Kiddy K. Asamoah & Francis T. Oduro & Ebenezer Bonyah & Baba Seidu, 2017. "Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).
    3. Abboubakar, Hamadjam & Kombou, Lausaire Kemayou & Koko, Adamou Dang & Fouda, Henri Paul Ekobena & Kumar, Anoop, 2021. "Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Joshua Kiddy K. Asamoah & Francis T. Oduro & Ebenezer Bonyah & Baba Seidu, 2017. "Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-23, July.
    5. Olumuyiwa James Peter, 2020. "Transmission Dynamics of Fractional Order Brucellosis Model Using Caputo–Fabrizio Operator," International Journal of Differential Equations, Hindawi, vol. 2020, pages 1-11, August.
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