Dissertation (MSc. Mathematics)In this work, Susceptible-Vaccination-Exposed-Infection-Treatment-Recovery mathematical model is proposed to study dog rabies disease transmission dynamics with vaccination and treatment in dog population group. Disease free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. Trace determinant technique was used to determine local stability of disease free equilibrium point while Lyapunov function technique was used to determine global stability of both, disease free and endemic equilibrium points. Basic reproduction number, R0, as well as herd immunity proportion were determined. Analytical solutions revealed that, the disease free equilibrium point E0 is locally asymptotically stable whenever R0 < 1 and unstable otherwise, while endemic equilibrium point E_ is globally asymptotically stable for R0 > 1. From numerical simulations, it was found that, basic reproduction number in presence of vaccination and treatment is R0 = 0.32 while R0 = 1.258 in the absence of these interventions. This implies that, the disease is stable to invade dog population for a long period of time in the absence of vaccination and treatment since R0 > 1. But unstable in the presence of these interventions because R0 < 1. The herd immunity proportion obtained is 20.5% which is the minimum dog population rate that should be vaccinated so that R0 will be reduced below the threshold value. Thus, vaccination and treatment are very potential measures for the disease control in dog population when effectively implemented as they were able to reduce R0 below the threshold value.