Several Kinds Of Worm Propagation Models Based On Different Medium

Worms,which take the network and various removable devices（computer,mobile phone,USB,hard disk）as the media,with their own replication ability,pose a serious threat to data security in the era of information and communication technology.Therefore,it is very important to study the propagation mechanism and predict the propagation trend of worms to prevent the spread of malicious worms.Mathematical model is an important tool for worm propagation analysis and control.In order to further understand worm propagation behavior and formulate effective defense strategies,three types of worm propagation models are studied in this paper.Firstly,a VEIQS worm propagation model with a new saturation incidence rate is established to study the propagation behavior of worms between computers through networks.The model takes vaccination and quarantine strategies into account.The threshold R₀ of the worm extinction is obtained by calculation,and the existence and stability of the two equilibria are demonstrated.After that,the accuracy of the theoretical results is verified by numerical simulation.Secondly,the worm propagation model between computers through USB devices is studied.The model consists of two sub-frames:computer and USB device.The next generation matrix method is used to obtain the basic reproduction number R₀.The Castillo-Chavez method is used to prove the global asymptotic stability of the disease-free equilibrium.In addition,in order to minimize the number of computers and USB devices carrying the worm virus in a short period of time,the worm propagation model is extended to include three control strategies.The feasibility of the theoretical results and the effectiveness of the control strategies are verified by numerical simulation.Finally,based on the above two types of models,the model of worm propagation between computers through networks and removable devices is studied.The basic reproduction number R₀ is obtained by using the next generation matrix method.Hurwitz criterion is used to prove the local asymptotic stability of disease-free equilibrium and endemic equilibrium respectively under R₀＜1 and R₀＞1.The global asymptotic stability of endemic equilibrium is proved by geometric method.In addition,sensitivity analysis is used to determine the relative importance of each parameter in worm epidemics,and corresponding control strategies are formulated accordingly.Then,using the Pontryagin maximum principle,the optimal control strategy is obtained which minimizes the control cost and the number of infected devices,and maximizes the number of recovered devices.