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

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 $\mathcal{R}_e < 1$, and unstable when $\mathcal{R}_e > 1$. Mesh and contour plots illustrate an inverse relationship between $\mathcal{R}_e$ and control strategies, including dog vaccination, health promotion, and post-exposure treatment. Increased intervention reduces transmission, while higher contact rates among dogs raise $\mathcal{R}_e$. Numerical simulations with optimal control confirm the effectiveness of integrated strategies. Vaccination and treatment are identified as key interventions for achieving rabies elimination within five years.