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

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  • 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, Hindawi, vol. 2025, pages 1-26, September.
    • Handle: RePEc:hin:jnljam:5559842
    DOI: 10.1155/jama/5559842
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