Dynamical Behavior Of Two Epidemic Models With A Nonlinear Incidence Rate

The dynamical behavior of two kinds of epidemic models SIRS with nonlinear incidence rate was studied. The following results were obtained .The first model with incidence rate kIS/1+αI~2 non-zero equilibrium state which is stable and no limit cycle.The second model with incidence rate kI~2S/1+αI, under certain conditions, has two nonzero equilibriums. The stability of equilibriums and the existence of limit cycle were studied. The bifurcation for the case of Bogdanov-Takens form was also studied.