This paper proposes deterministic epidemic modeling of future botnet malware named self-evolving botnets, assuming a contact process. The self-evolving botnets discover vulnerabilities of hosts by exploiting the computing resources of infected hosts, which could become serious threats to the future Internet society. The proposed epidemic model represents their infection dynamics on an overlay network consisting of hosts. It predicts the infection spreading of the self-evolving botnets with the use of mean field approximation using the degree distribution of the overlay network. Through numerical calculations, we show that the proposed epidemic model well approximates the infection spreading in short time.