The Qualitative Analysis Of Two Kinds Of Linear Infection Rate Of Infectious Disease Model With The Incubation Period

Infectious disease dynamics is a new discipline,in the research of infectious disease,we usually combine with mathematics,mathematical model is established to analyze the influence of each factor of infectious diseases,and then to the progress and epidemic of the disease carry on effectively forecast,and timely prevention and control.Based on the analysis of the transmission mechanism of infectious diseases,then stablish two types of infectious disease model with the incubation period,analyze the model using the qualitative and stability theory of ordinary differential equation, and then get the basic reproductive number of the disease would be endemic point,and the global stability of the disease-free equilibrium point and the endemic equilibrium point.In the introduction introduce the research and development present situation of the infectious disease model with the incubation period and the practical significance of the research of this paper.In the second chapter,this paper introduces the basic concept of the infectious disease dynamics,and the basic knowledge of this subject.In the third chapter,the following research with the incubation period of infectious disease model,find out the basic reproductive number,and discuss the existence and stability of the disease-free equilibrium point and the endemic equilibrium point. First of all prove the existence of the equilibrium point,and then using the Hurwitz criterion get disease-free equilibrium point of local asymptotic stability.At last,through the model dimensionless changes,get the global stability of the equilibrium point. In the fourth chapter,the following research with the incub ation period of infectiousdisease model,find out the basic reproductive number,and discuss the existence and stability of the disease-free equilibrium point and the endemic equilibrium point. Prove the existence of the equilibrium point and the local stability of the disease-free equilibrium point,get the global stability of the equilibrium point.