Dynamic Analysis Of Delay Epidemic Model With A Nonlinear Incidence Rate

The dynamic mode l of infectious diseases is an important too l for the study ofinfectio us diseases. The class ic compartme nt modeling method is used to study thetwo SIRS epidemic model with time de lay. First we research a nonlinear infectionrates and temporary immunity Delay SIRS model; Second, research with a doubledela y SIRS model us ing the basic theory of d iffere ntia l equations dyna mica lproperties of the two models were analyzed.This thes is is divided into four chapters:The first chapter outlines the process of the model study o f infectious diseases,the ma in contents of the s ignificance of this study.The second chapter, the main content is given in this paper used the De layDifferentia l stability, other aspects of basic methods and theore ms.The third chapter, the ma in cons ideration establis hes the appropriate SIRSEpide mic Model with no nlinear inc idence rate and temporary immunity case. Thro ughtheoretica l analys is, we get the model basic reproductio n number of d isease-freeequilibrium and endemic equilibrium, and gives loca l and global asymptotic stabilityof the disease-free equilibrium and the endemic equilibrium cond itions.Chapter IV, both late ncy and temporary immunity SIRS epidemic model withtwo delays is studyed. By theoretical ana lys is, we give the model of the basicreproduction number and types of equilibrium point, and the stability conditions ofthe two types of equilibrium point.