Your question format is a little confusing for me because you are very specific about "web application design patterns using mod_perl"
As I understand design patterns, they are not specific to a programming language, web programming or mod_perl, but higher-level computer science concepts.

With that said, there is a great wiki with Perl implementations of design patterns, although I'm not sure which will apply to your specific webapp or mod_perl.
http://perldesignpatterns.com/perldesignpatterns.html That page has pretty much every design pattern that I've ever heard of, and then some. Hope that helps.