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In this book, the dynamical behavior of some epidemiological models is investigated. Two types of epidemiological models involving vaccine and immigrants those which may contain infected individuals are proposed and analyzed. The first chapter proposed model represents SVIR epidemic model in which the infectious disease transmitted directly by contact between susceptible and infected individuals using standard mass action incidence rate. While, the second chapter proposed model represents SVIRS epidemic model in which the infectious disease transmitted, through external sources in the environment in addition to the direct contact between susceptible and infected individuals, using simple mass action incidence rate. Both the models are represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of these two models are investigated. The local and global stability conditions of all possible equilibrium points are established. The occurrence of local bifurcation and Hopf bifurcation near each of the equilibrium points are discussed.