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Botnets have become the most sophisticated and dangerous way of spreading malware. Their damaging actions can range from massive dispatching of e-mail messages, to denial of service attacks, to collection of private and sensitive information. Unlike standard computer viruses or worms, botnets spread silently without actively operating their damaging activity, and then are activated in a coordinated way to maximize the ``benefit'' of the malware. In this paper we propose two models based on compartmental differential equations derived from ``standard'' models in biological disease preading. These models offer insight into the general behavior of botnets, allowing both the optimal tuning of botnets' characteristics, and possible countermeasures to prevent them.