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This I don't know about. Recently, there has been spyware that has trojans in them
True. But spyware finds its way onto a system by masquerading as something else (i.e. CoolWebSearch). I am not implying that the user must first be aware of the fact that they are installing a trojan. Spyware in this manner does not continue to infect more files on the system once its payload has been delivered either. To infect another computer, it must again be downloaded from a fileserver somewhere and installed on another system. A server/client infection technique, where a virus uses a peer to peer method.