Malicious code, which is designed to probe for weaknesses and spread by constantly attempting to infect systems, will not go away or stop its activity once you have protected or patched your system.
The only way to stop the probes is by using something to filter them out, at the firewall or gateway level, as you suspected. Otherwise, they will continue to seek out weaknesses in your system and nothing you do at the desktop level will have any impact on them.
For example, I got tired of Sircam and Yaha-infected mail coming to me. I used a spam filter on the mail server to block incoming mail containing subject lines which correspond to these messages. Voila, no more infected e-mails of that type. The same idea can be applied to your case.
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This was first published in February 2003