We study the well-known SIR (susceptible, infected, recoverd) model with nonlinear complex incidence rates. Firstly,a series of coordinate transformations are carried out to change the equations as the amenable Hamiltonian systems. Secondly the Melnikov's method is used to establish the conditions of existence of chaotic motion and find the analytically critical values of homoclinic bifurcation. Good agreement can be found between numerical results and analytical results.