Research Article published by Asian Journal of Mathematics and ApplicationsRabies is one of the neglected tropical diseases that has persisted for centuries in Ethiopia, and it is endemic within and around Addis Ababa. For the purpose of studying the dynamics of the disease we propose a deterministic mathematical model with human, dog and livestock populations and formulated as a system of ordinary differential equations. Basic reproduction number 0 R and effective reproduction number e R are computed using next generation operator. Sensitivity analysis of e R shows the natural death rate of dogs 𝜇𝑑 , the annual birth rate of dogs 𝜗𝑑 , dog-to-dog transmission rate 𝛽𝑑 , and disease induced death rate 𝜎𝑑 are found to be the most sensitive parameters of e R . According to numerical simulations of our system rabies transmission will increase within and around Addis Ababa, and may peak in 2024 and 2026 in human and livestock populations respectively. Our simulation shows that 25% vaccination coverage in livestock populations will reduce the future infection by half. This study suggests that a combination of interventions consisting of 60% of vaccination coverage in dog populations, 15% culling of stray dogs, and reducing annual crop of newborn puppies by 25% will reduce the number of human and livestock infections by 70%, and the disease will be eradicated from the community.