Modification And Analysis Of SIRA Computer Virus Model

With the rapid development of the Internet,the services and applications relating to network and data being exploding,and at the same time network security risks and problems have becoming more and more severe.Computer viruses have the ability to self-replicate and spread,and are destructive to the users,which have caused people to fear and are widely regarded as the number one enemy of network security.In view of the similarity of the transmission mechanism between computer viruses and biological viruses,people often apply infectious disease dynamics modeling ideas to study computer viruses,in order to investigate its transmission behavior,so as to deepen the understanding of the virus at a macro level.The early mathematical models proposed by people include SIS model,SIR model,SEIR model,SIRA model and so on.Later,people refined computer virus modeling further,for example,taking into account the impact of user's awareness,virus hierarchical immunity,and time delay on the spread of computer viruses,so as to modify it.In this dissertation,we research the influence of user's awareness and hierarchical immune rates on SIRA model,and theoretical analysis and numerical simulation of the resulting model.Firstly,considering that computer users are subjectively aware of viruses,their effects can be compared to vaccination in the prevention and treatment of infectious diseases.Based on this understanding,we introduced a linear user awareness intensity function in the SIRA model to obtain a SIRA model with user awareness.The non-negativity of the SIRA model with user awareness and the stability of the non-toxic equilibrium point and the toxic equilibrium point are theoretically demonstrated,and the theoretical results are numerically simulated by Matlab.The results of the research indicate that the stability of the system improves with the increases of user awareness.Secondly,since anti-virus software and other defense measures,both uninfected computers and infected computers can obtain “immunity” to a certain extent(usually the latter is often stronger than the former).Based on this understanding,we introduced the hierarchical immune effects in the SIRA model to obtain the SIRA model with hierarchical immune rates.The non-negativity of solutions of SIRA model with hierarchical immune rates and the stability of the non-toxic equilibrium and toxic equilibrium are theoretically demonstrated.The theoretical results are numerically simulated by Matlab.The research results show that the system will be more stable under the hierarchical immune effects.