Sirolimus for Eosinophil-Associated Gastrointestinal Disorders

Background: * Eosinophil-associated gastrointestinal disorders (EGID) are a group of related disorders that affect the esophagus, stomach, and bowel. There are two major types of EGID, eosinophilic esophagitis and eosinophilic gastroenteritis. They are caused by the body's immune system being activated by food allergens, which then damages the gut wall. People with EGID have large numbers of eosinophils (a type of white blood cell) in their gut. EGID can cause difficulty swallowing, abdominal pain, or nausea. * At present, there are no drugs specifically approved to treat EGID. Most adults who have EGID receive steroid therapy to manage the symptoms. However, long-term steroid use may cause other problems in the body. Researchers want to see if low-dose sirolimus can be used to treat EGID. Sirolimus is a drug used to prevent rejection of transplanted organs. It may be able to keep the body's immune cells from being activated by food allergens and decrease the eosinophils. Objectives: \- To see if low dose sirolimus is safe and decreases blood or gut eosinophils in EGID. Eligibility: * Individuals between 18 to 65 years of age who have EGID. * Participants must also have an elevated blood eosinophil count and positive blood tests for IgE antibodies to foods. Design: * Participants who are on medicine for EGID or related symptoms must be on a stable dose for 1 month before screening and stay on that dose throughout the study. * Participants will be screened with a medical history and physical exam, and review their symptoms. They will provide blood and urine samples. They will also have heart and lung function tests. Some participants may have allergy skin tests. * At the first study visit, participants will have 2 days of inpatient tests. They will repeat the tests from the screening visit. They will also have a full analysis of the esophagus, stomach, and small intestine. On the second day, they will start to take sirolimus as a liquid with orange juice or wa