This research article published by the International Journal of Advances in Scientific Research and Engineering, Volume 5, Issue 9, September - 2019Rabies is a zoonotic, viral disease that causes acute inflammation of the brain in humans and other mammals. It is transmitted by the saliva of infected animals via bites, scratches or contact between open body parts of infectious dog and noninfectious. In this paper, we have analysed a SEIV (Susceptible-Exposed-Infectious-Vaccinated) mathematical model for dog-rabies whereby sensitivity analysis and numerical simulation of the model have been carried out, presented and discussed. According to the sensitivity indices of parameters used at DFE (Disease Free Equilibrium) point, an infection rate of stray dogs is the most positive sensitive parameter while the natural death rate of stray dogs is the most negative sensitive parameter. These results lead us to the advice of putting much effort on these parameters when fighting against rabies disease transmission. Based on the numerical analysis results, it is advised to use mass vaccination of stray dogs as a strategy to fight against dog rabies transmission. Sensitivity analysis was done by using MATHEMATICA and the numerical simulation of the basic model was done by using ode45 MATLAB’s standard solver for ordinary differential equations (ODEs). All analysis results were obtained by using data collected from Mbwa wa Africa and the Ministry of Agriculture, Livestock Development and Fisheries of the United Republic of Tanzania (URT).