Transmission Dynamics Of A Class Of SIR Models To Computer Virus

Computer virus has been always accompanied by the use of computers and its impact on human life has become increasingly obvious. Although we can use various methods to kill the virus, it is difficult to prevent the spread of the virus. In order to control the spread of computer virus, many experts and scholars have researched its transmission mechanism. Similar to the propagation of biological virus, we can use some principles of infectious disease models to formulate the transmission ones of computer virus, and then exhibit some reasonable explanations about the spreading phenomena of computer virus, which will help us better understand the infection process of computer virus, in order to more effectively prevent and control the virus.The purpose of this paper is to study some SIR models to the computer virus with the different spreading patterns in the homogeneous spaces, where S, I and R represent the densities of susceptible, infected and recovered individuals in computer,respectively. We will introduce the relevant concepts of infectious disease dynamics before establishing the model, and systematically investigate some problems about virus change trends in the models. We will give out the long-time behaviours of S,I and R, that is, the corresponding transmission dynamics of models. This paper consists of the following five chapters:The first chapter introduces some background of virus, literature sources and results obtained in the current references. We will combine the characteristics of computer viruses with other factors to build three SIR models with different patterns of transmission. For these factors, we not only consider the spatial diffusion of the virus, but also pay attention to the changes of infected area over time, which make our models more match the propagation of virus in the reality;4In the second chapter, we use a spatially-independent system of ordinary dif-ferential equation to construct the SIR model. The threshold R0 of this model- an important index in the epidemic-is given out, and the local stabilities of the disease-free equilibrium and the epidemic equilibrium are also discussed according to the value of R0.In the third chapter, we consider that the spread of the virus is not only related to the time, but also to the space, so we incorporate the spatial diffusion into the model, and then adopt the reaction diffusion equations with homogeneous Neumann boundary conditions to describe the transmission of the virus. In this model, still centering on the threshold R0, we obtain the local stabilities of the disease-free equi-librium and the epidemic equilibrium as well as further get those global stabilities under other conditions.In the fourth chapter, we introduce the free boundary condition, which is based on the fact that the area infected by virus is changing with time. The threshold R0F (t) of such an SIR model with free boundary is a function with respect to t, which is different form the constant R0 in the two chapters above. We combine such a threshold with other relevant conditions to explore the sufficient conditions about the gradual vanishing of virus.In order to make our theoretical results more intuitive, some numerical simula-tions will be carried out in the final chapter, which can further confirm our theoretical findings. At the same time,we will also exhibit some explanations of the transmis-sion dynamics for the above different SIR models. It is concluded that the related infectious diseases parameters play a decisive role in the spread of the virus, and it means that the more attention to the parameters people pay, the more effectively they control the spread of the computer virus.