In the present paper, We discussed a Susceptible-Exposed-Infected-Susceptible typhoid fever mathematical model. Obtained disease-free and endemic equilibria and  basic reproduction number R()  for the model.  Local and global stability  studied for both equilibrium points using Routh–Hurwitz criteria ,Castillo-Chavez criteria and Lyapunov-Lasalle principle respectively . Case study   also be done numerically and graphically which showed that how the disease will be dies out and when the disease will persists.

Keywords: Typhoid , reproduction number, Routh–Hurwitz criteria ,Castillo-Chavez criteria , Lyapunov-Lasalle principle.