Research On Hopf Bifurcation Of Delayed Network Virus Propagation Model With Hierarchical Infection Rate

With the advent of the "Internet +" and "Internet of Things" eras,computer technology is developing rapidly,and advances in computer network technology have also brought about the rapid spread of network viruses.In history,network viruses have brought huge losses to all aspects of human society,especially economic aspects,causing extreme panic.Now,with the introduction of smart wearable devices,the losses caused by network viruses are not only economic,but also pose a threat to human body,mind and economy.To combat network viruses,people have adopted a series of control strategies,such as assembling anti-virus software,reinstalling operating systems,etc.,but these measures have lagged behind the emergence of viruses.Because of the unpredictability of network viruses,a comprehensive understanding and analysis of the spreading rules and characteristics of network viruses,establishing a more realistic network virus spreading model,and formulating effective control strategies for network virus spreading are effective means of controlling virus spreading.It is a key subject of network virus dynamics research.This paper aims to comprehensively analyze the law of network virus transmission,establish a more realistic new network virus transmission model,and propose two timedelay models with hierarchical infection rates.The main research results are as follow:(1)Propose model 1: SEIRS model.Both the latent state node and the outbreak state node in this model have the infection ability and have different infection rates.The model considers the latency of the network virus,the time period required for antivirus software to clean up the network virus,and the time period of the temporary immune period for the node to recover.The different combinations of latency in the model,the time period required by anti-virus software to clean up network viruses,and the time delay in recovering the state node's temporary immune period are used as bifurcation parameters.The existence and locality of the Hopf bifurcation generated by the model are discussed.Asymptotic stability.The properties of Hopf bifurcation are studied using the central manifold theorem and canonical theory under the condition that the three delays are not equal.Finally,the simulation results are used to verify the results.(2)Propose model 2: SEIQRS model.Inspired by infectious disease control methods,the isolation strategy is further considered on the basis of the SEIRS network virus propagation model,and the latent state node and the outbreak state node in the model have different infection capabilities.The existence of Hopf bifurcation in the model is discussed by using different combinations of the latency of the network virus and the temporary immune period of the recovery node as bifurcation parameters.In the case where the two time delays are not equal,a calculation formula for determining the Hopf bifurcation property is derived.Finally,the simulation results are used to verify the results.