The Studies Of SIQR Epidemiological Models With Saturated Contact Rates

This article in the previous study of infectious disease model is proposed on the basis of thethree class with saturation incidence of infectious disease dynamics model, and proves the modelstability.Based on the model of infectious disease research background, this paper addresses theresearch present situation and the basic concepts and theorems, lemmas are briefly presented. Atthe same time, we have to do the main work.Secondly, it presentes with constant input and saturation incidence SIQR infectious diseasemodel，applies differential equation theories knowledge to this model carried on analysis andresearch systematically, makes use of the characteristic root method, construct whether Liapunovfunction and LaSalle invariance principle and Bendixsen-Dulac criterion, in order to prove thelocally stability and the global stability,and gets the liminal value,discussed the existencecondition of the disease-free equilibrium and the endemic equilibrium. Then, according to theactual situation, it puts forward the corresponding prevention and control method.Then, it puts forward a class of vertical infection and vaccination in the SIQR epidemicmodel, gives the liminal value of the disease persistence and extinction thresholds. Using Lasalleinvariance principle, LiaPunov function, Hurwith criterion is proved that the disease-freeequilibrium and the endemic equilibrium is global stability.Finally, establishment and analysis of a class of vertical transmission and pulse vaccinationin the SIQR epidemic model, the Floquet multiplier theorem and comparison theorem, provesthat the disease-free periodic solution is existence and global stability; and obtain sufficientconditions for the permanence of the system.