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Modeling and analysis of the effects of antivirus software on an infected computer network. (English) Zbl 1364.68064
Summary: In this paper, a nonlinear mathematical model for cleaning an infected computer network by using antivirus software is proposed and analyzed. In the modeling process, the total number of nodes in the network are divided in three subclasses, namely, the number of susceptible nodes, number of infected nodes and the number of protected nodes. A variable representing the number of antivirus softwares, assumed to be proportional to number of infected nodes, is also considered in the model which interacts with other nodes bilinearly to conduct the cleaning process. The model is analyzed by using stability theory of differential equations and computer simulation. The analysis shows that it is possible to clean the computer network under certain condition which depend upon the inflow rate of infected nodes in the computer network, the rate of interaction of infected nodes with susceptible nodes and their interactions with antivirus software, etc. It is found that the entire network can be cleaned eventually if the antivirus software is applied on the network, where a separate class of protected nodes is formed. The computer simulation confirms the analytical results.

##### MSC:
 68M10 Network design and communication in computer systems 34D20 Stability of solutions to ordinary differential equations
##### Keywords:
computer network; infected nodes; virus; antivirus
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##### References:
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