Using a complex mathematical model, we investigated the worldwide stability of rabies transmission in depth in this work. Six separate compartments were created from the dog population: immune-compromised dogs, vulnerable dogs, exposed dogs, infected dogs with a furious infection, infected dogs with paralysis, and recovered dogs. After building the model, we used the Volterra-Lyapunov approach to show diagonal stability by carefully analyzing the system's equilibrium points. Additionally, we determined the critical, sensitive characteristics that might be targeted to successfully stop the disease’s spread. MATLAB was used to conduct numerical simulations to validate our findings, yielding robust outcomes and conclusions.