An approximate evaluation of the conditions for the termination of a computer virus epidemic in connected networks associated with random graphs

Mathematical modeling of computer virus epidemics is the most important area of theoretical research in the field of information security. This paper examines a Markov model of the computer virus spread based on the Reed–Frost model. The main aim of the article is to analyze the applicability of the modified Reed-Frost model to the class of networks associated with random Erdos-Renyi graphs. In particular, the effect of the ratio of the probability of cure to the probability of infection on stopping the spread of a computer virus was tested. The results of this model are compared with ones obtained via the simulation modeling for different values of epidemic parameters and network characteristics. In the calculations and experiments carried out, the following parameters changed: the probability of infection, the probability of cure, as well as the connectivity of the network. The Wolfram Mathematica symbolic computing system was used for calculations. A C++ program written earlier by the author and their supervisor was used to conduct the computational experiment. The studies show that, under certain parameters, the condition for ending the epidemic is confirmed by both theoretical calculations and experimental results. However, the epidemic vanishes before the threshold value calculated is reached. In the future, the author plans to give a more accurate theoretical assessment of the conditions for ending the epidemic.

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