Global Analysis Of An SIQ Epidemic Model With Non-linear Incidence Rate

Mathematical model is established in infectious disease dynamics, which is based on some kind of disease occurrence, development, influence factors, environmental changes, etc.Dynamics characteristic of model is analyzed, to reflect the popular trend and the change rule of disease, so as to find the optimal method for preventing effectively and controlling the disease.In this paper we studied the global stability of an isolation SIQ epidemic model with non-linear incidence rate, and an epidemic model on avian influenza(H7N9) which was established in the article to investigate the impact of media on the spread of infectious diseases; and the basic reproduction number 0R was obtained, and the disease-free equilibrium and endemic equilibrium was obtained too.By means of Lyapunov function method, Hurwitz criterion and La Salle’s Invariable Principle, the global stability of the disease-free equilibrium and endemic equilibrium was proved.In the introduction, the research background and basis of the infectious disease model with isolation was introduced, and an epidemic model on avian influenza(H7N9) is established in the article to investigate the impact of media on the spread of infectious diseases, the research purpose and significance, the research status and prospects, as well as the content and practical value of this thesis was introduced.In the second part, some basic concept and knowledge from Ordinary Differential Equation Method of Qualitative and Stability, as well as Dynamics of Infectious Diseases, relating to this paper, was introduced.In the third part, global analysis of an SIQ epidemic model with non-linear incidence rate was studied, the threshold about whether the disease being popular or not was obtained. The existence and stability of the disease-free equilibrium and endemic equilibrium was gained.In the fourth part, an epidemic model on avian influenza(H7N9) is established in the article to investigate the impact of media on the spread of infectious diseases, and the basic reproduction number of models is obtained.The existence and stability of the disease-free equilibrium and endemic equilibrium was gained.In the five part, the main research results of this paper was summarized, and a further outlook of researching topics of this article was made.