Abstract:

Based on the epidemic dynamic theory, a SIRS epidemic model with logistic growth and treatment was established. On the basis of the growth of the total population satisfying Logistic equation and nolinear differentiable function being the treatment term, the model describes the effect of limited medical resources to delaying treatment of the sick. Based on the RouthHurwitz criterion, LaSalle invariant set principle and structured proper Lyapunov function method of stability theory in the differential equation, global asymptotic stable algebraic criterion of diseasefree equilibrium and endemic equilibrium
 and backward bifurcation conditions of the model were obtained. The research results show when the delayed effect is serious, backward bifurcation will take place and the basic reproduction number is not the threshold value of the eradicating of the disease. In order to eradicating the disease, medical resources construction should be strengthened, and prompt and superior medical service should be provided.

Key words: SIRS epidemic model, staurated treatment function, backward bifurcation, global stability