liability of moth infestation

Tenancy Types and Management

My tenant has been in the flat for 18 months and has recently reported an infestation of moths.
There was no pre-existing condition in the ten years I have owned the flat. Her room is small and infrequently dusted or hoovered and she always keeps the blind down.  The carpet has been quite damaged but there is no damage to the bed.
Am I liable as a landlord to fumigate, replace beds, carpet etc.  I imagine it would be sensible to change the bed even if there is no evidence given the eggs might be harboured there.
I provide beds, sofas, chairs and tables although the flat is not let as a furnished one per se (i.e.the fact that it is furnished it is not referred to in their contract).
Thanks for your advice.