Research On Some Problems Of Three Types Of Infectious Disease Models

With the intensification of environmental pollution and the enhancement of the resistance to pathogens,the incidence of infectious diseases is becoming more and more frequent,and even some of the infectious diseases that have been controlled have become popular again.Therefore,it is of great significance for human society to master the pathogenesis and transmission mechanism of infectious diseases and make effective measures to control and prevent the occurrence and spread of infectious diseases.Since it is impossible to experiment on human beings when studying infectious diseases,it is an important way to establish a mathematical model of dynamic behaviors of infectious diseases.In this paper,three types of infectious disease models are studied,and the dynamic properties of these models are analyzed to understand the transmission characteristics of infectious diseases.Firstly,a class of discrete SI infectious disease models with impulse and multiple delays are investigated.The discrete model is based on the original continuous SI model and built by Euler method.According to the definition of model persistence,the persistence of the discrete model is proved,the sufficient condition of the model persistence is given,and the persistence of the model is verified by numerical simulation.Secondly,a class of discrete SIS infectious disease model with delay term is discussed.The discrete model is based on the original continuous SIS model and built by the Euler method.The condition of the model has a positive equilibrium point is given.By analyzing the characteristic equation,the stability of the equilibrium point and the condition of producing the Neimark-Sack bifurcation are given,and the correctness of the conclusion is verified by numerical simulation.Finally,a class of integral and partial differential form SIS infectious disease model with age structure is studied.The meshless interpolation method is applied for this model and obtains the discrete form for numerical solution of this model.Furthermore,the stability of the method is analyzed.The effectiveness of the method is verified by experimental examples.