Final answer:
Churg-Strauss syndrome is the most likely cause of the combination of adult onset asthma and peripheral neuropathy. It involves asthma, eosinophilia, and vasculitis affecting small to medium-sized vessels, and is characterized by a hypersensitivity reaction with eosinophil involvement.
Step-by-step explanation:
The combination of adult onset asthma and peripheral neuropathy is suggestive of Churg-Strauss syndrome, also known as eosinophilic granulomatosis with polyangiitis. This condition is characterized by asthma, eosinophilia, and systemic vasculitis affecting small to medium-sized vessels, and is associated with peripheral neuropathy. It is one of several potential causes of asthma and peripheral neuropathy, but it is specifically characterized by a hypersensitivity reaction and the involvement of eosinophils in the inflammatory process. In contrast, sarcoidosis is a systemic inflammatory disease that forms non-caseating granulomas but isn't typically associated with peripheral neuropathy.
Rheumatoid arthritis, which is a common inflammatory joint disease involving type III hypersensitivity reactions, and systemic lupus erythematosus (SLE), which can affect various tissues and organs, are less likely to be associated with asthma and peripheral neuropathy as primary symptoms.