In this thesis, an epidemic model with nonlinear incidence rate is investigated. The ranges of the parameters involved in the model are given under which the equilibria are positive. By carrying out the qualitative behaviour analysis, it is shown the disease free equilibrium can exhibit saddle-nodes, saddle point or stable node depending on the ranges of the parameters. It is shown that the interior equilibria are saddle point, stable or focus nodes. Furthermore, several numerical solution and graphics are given to support the theoretical analysis.