| This paper studies the SIQS and SIQR infectious disease models with quarantine items under the influence of media reports.For the SIQS infectious disease model,we introduce the segmentially smooth media influence function.Firstly,the Lambert W function is used to obtain the expression of the equilibrium point,and thenR0（27）1 andR0（29）1 linearization method,Bendixson-Dulac criterion and true and false equilibrium state are used to analyze the local and global stability of the equilibrium point.Finally,the global stability of the equilibrium point is verified by numerical simulation and the effectiveness of the media report and isolation strategy is demonstrated.For SIQR infectious disease model,we introduce six different forms of media influence function to obtain SIQR and SIQRM infectious disease model of exponential form media influence function,SIQR and SIQRM infectious disease model of Holling Type II media influence function and SIQRM infectious disease model of media influence function e-α1I-α2M and SIQRM infectious disease model of media influence function 1/（1+α1I+α2M）.Firstly,the expression of the equilibrium point of SIQR model in different forms is obtained respectively.Then,the existence of the equilibrium point is analyzed by the basic reproduction number 0R,and the local stability of the equilibrium point is analyzed by linearization method and Routh-Hurwitz criterion respectively.Then,the local stability of the equilibrium point was verified by numerical simulation,and the transmission of the disease could be controlled by media reports and quarantine measures.Finally,different media influence functions m were numerically simulated under different media influence factors,indicating that different media influence functions had different inhibitory effects on disease under different media influence intensities.The sensitivity analysis of basic reproduction number 0R was completed to understand the influence of model parameters on epidemic transmission. |
