Applied Mathematics & Information Sciences

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Since the number of compromised computers, or botnet, continues to grow, the cyber security problem has become increasingly important and challenging to both academic researchers and industry practitioners. A respect to combat botnet propagation is to understand the attacker’s behaviors based on the whole operation of a system that can be modeled with population models used in epidemiological studies. In this paper, we treat the interaction between the botnet herder and the defender group as a modified SIS epidemic model with external entrance and allowing computers of undetected states. Based on optimal control theory, we derive the optimal strategy of the botnet herder as a feedback on the rate of infection under given levels of entrance and defense. The obtained optimal policies dynamically evolve with time and offer useful insights for ultimately solving the botnet defense problem.

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