Chaos for a class of complex epidemiological models
一类复杂流行病学模型的混沌研究

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.