aeluromania

aeluromania, ailuromania, eluromania 1. An absurd desire to have many cats to such a degree that some people have been known to have dozens of cats in an apartment or house. 2. An intense enthusiasm for having many cats around; sometimes, even when conditions are not suitable for their existence. 3. An abnormal love of cats.
Found on http://www.wordinfo.info/words/index/info/view_unit/42/
No exact match found