By means of asymptotically stable theory and infection model theory of ordinary differential equation, we do research on SIQS model with nonlinear and isolation. Firstly, we obtain the existence of threshold value R0 of disease-free equilibration point and local disease equilibration point. Secondly, we prove disease-free equilibration point is locally asymptotically stable when R0 < 1, and local disease equilibration point is locally asymptotically stable when R0 > 1. Furthermore, we have disease-free equilibration point and local disease equilibration point are globally asymptotically stable with the help of Liapunov function. Lastly, we explain at the point of biology.