Research On Infectious Disease Model Affected By Random Noise And Synchronization Analysis

The spread of infectious diseases has always attracted people’s attention.In order to deeply understand the spread law of infectious diseases,at present,a large number of mathematical models of infectious diseases have been established and qualitative and quantitative studies have been carried out on them,now deterministic infectious disease models have been widely studied,in fact infectious disease transmission is a process influenced by random factors,and the deterministic system does not consider obviously random factors,so it is better to describe the epidemic process of infectious diseases with stochastic model.In the first chapter,it is more practical to study the dynamical behavior of the stochastic infectious disease system under the disturbance of environmental noise.On this basis,we establish a suitable mathematical model of infectious disease transmission to explore its internal transmission mechanism and forecast its development trend.In the second chapter,a stochastic delay model with specific functional response is constructed to study the transmission of an infectious disease by vertical transmission and vaccination.Firstly,the existence and uniqueness of positive solutions of the model are proved.Secondly,the sufficient conditions for the extinction and persistence of the model are analyzed.Finally,the numerical simulation verifies that the results of the stochastic system are close to the deterministic system when the white noise is small,but different phenomena will appear when the white noise is large enough,the white noise can restrain the spread of infectious diseases.In addition,the increase of vaccination rate and time delay has certain influence on the development of infectious diseases,and can effectively restrain the occurrence of infectious diseases under appropriate circumstances.In the third chapter,we construct a synchronization model of infectious disease to study the relationship between the spread of infectious diseases and the collective behavior of individuals in response to infectious diseases by applying the adaptive mechanism observed in real networks and adding appropriate controllers to the nodes in the complex network affected by noise.The relationship between infection rate and synchronization stability is studied,and the global stability condition of the synchronization model in the sense of mean square is obtained.The theoretical results are verified by numerical analysis,it is found that the existence of synchronous information can make individuals show collective behavior,and the collective behavior of individuals can inhibit the transmission behavior of infectious diseases,at the same time,the spread of infectious diseases can accelerate the collective behavior of individuals.