Abstract:A dynamic model of the initial innate system response to a lung infection is considered. firstly, the condition that the model has a positive equilibrium point is obtained based on the discriminant of the roots of the cubic polynomial equation, secondly, the specific type of positive equilibrium point of the model and the stability of the positive equilibrium point under the condition are discussed by using the theory of the equilibrium point stability and the theorem of the central manifold, and finally, the emergence of a saddle-node branching at the equilibrium point is considered.