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A Mathematical and Optimal Control Model for Rabies Transmission Dynamics Among Humans and Dogs With Environmental Effects

Author

Listed:
  • Mfano Charles
  • Sayoki G. Mfinanga
  • G. A. Lyakurwa
  • Delfim F. M. Torres
  • Verdiana G. Masanja

Abstract

This study presents a deterministic model to investigate rabies transmission dynamics, incorporating environmental effects and control strategies using optimal control theory. Qualitative and quantitative analyses reveal that the disease‐free equilibrium is stable when the effective reproduction number Re 1. Mesh and contour plots illustrate an inverse relationship between Re and control strategies, including dog vaccination, health promotion, and postexposure treatment. Increased intervention reduces transmission, while higher contact rates among dogs raise Re. Numerical simulations with optimal control confirm the effectiveness of integrated strategies. Vaccination and treatment are identified as key interventions for achieving rabies elimination within 5 years.

Suggested Citation

  • Mfano Charles & Sayoki G. Mfinanga & G. A. Lyakurwa & Delfim F. M. Torres & Verdiana G. Masanja, 2025. "A Mathematical and Optimal Control Model for Rabies Transmission Dynamics Among Humans and Dogs With Environmental Effects," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:5559842
    DOI: 10.1155/jama/5559842
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    References listed on IDEAS

    as
    1. C. S. Bornaa & Baba Seidu & M. I. Daabo, 2020. "Mathematical Analysis of Rabies Infection," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-17, March.
    2. repec:plo:pone00:0020891 is not listed on IDEAS
    3. repec:plo:pntd00:0007582 is not listed on IDEAS
    4. C. S. Bornaa & Baba Seidu & M. I. Daabo, 2020. "Mathematical Analysis of Rabies Infection," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    5. Demsis Dejene Hailemichael & Geremew Kenassa Edessa & Purnachandra Rao Koya & Theodore E. Simos, 2022. "Effect of Vaccination and Culling on the Dynamics of Rabies Transmission from Stray Dogs to Domestic Dogs," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-14, September.
    6. Mussa A. Stephano & Jacob I. Irunde & Maranya M. Mayengo & Dmitry Kuznetsov & Arvind Kumar Misra, 2024. "The Significance of Stochastic CTMC Over Deterministic Model in Understanding the Dynamics of Lymphatic Filariasis With Asymptomatic Carriers," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-11, May.
    7. Demsis Dejene Hailemichael & Geremew Kenassa Edessa & Purnachandra Rao Koya, 2022. "Effect of Vaccination and Culling on the Dynamics of Rabies Transmission from Stray Dogs to Domestic Dogs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    Full references (including those not matched with items on IDEAS)

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