Model of The Dynamics of the Spread in Computer Networks of Evolving Viruses, Subject to Obsolescence and Lag in the Action of Protection

The paper considers creating of the dynamic model of the stochastic spread of evolving viruses in the address space of computer networks, subject to obsolescence and lag of antivirus. The evolutionary properties of viruses are taken into account in the model by the formal rule that previously immunized or cured nodes, at some interval (the size of which is the model parameter), can be re-infected, and exposure of antivirus protection has a lag time (also is a model parameter). In this model, it was accepted that any network node could be in one of three states: in a protected (immunized) state; in an infected state; in a neutral state. In a neutral state, the node may be infected or immunized. In an immunized state, the node can send out antiviruses, which cures infected and immunizes neutral nodes. In this state, copies of antiviruses (useful viruses) are sent out to the nodes of the network randomly chosen (random choice in the address space indicates of the stochastic behavior). In an infected state, the node can send out copies of viruses to nodes in the network, also by randomly selecting in the address space (this also shows the stochastic behavior). The stochastic dynamics model of the spread of evolving viruses in the computer network was described graphically using a diagram of possible transitions between nodes states which allow one to create a system of kinetic differential equations describing these processes. One of the advantages of the model being developed is the ability to modify and expand it by creating more complex state change graphs and transitions between them. This provides supplementing the system of kinetic equations with a member that considers the overall increasing in the number of users and devices in computer networks over time that can be described by a function of any kind.