A Study of Topical BX005-A in Subjects With Moderate to Severe Atopic Dermatitis

Inclusion Criteria: 1. Male or female ≥ 18 years old 2. Confirmed clinical diagnosis of active AD with at least a 6-month history and clinically stable AD for ≥ 1 month 3. Clinical diagnosis of moderate or severe AD with a vIGA-AD score of ≥ 3 and a lesion vIGA-AD score ≥ 3 in the target AD skin lesion 4. BSA with AD of 2%-30%, excluding scalp 5. Colonized with S. aureus in at least one AD skin lesion 6. Female subjects of non-childbearing potential must meet at least 1 of the following: postmenopausal status; documented hysterectomy and/or bilateral oophorectomy; or medically confirmed ovarian failure. All other female subjects (including those who have undergone tubal ligation) are of childbearing potential. 7. Female subjects of childbearing potential who have a negative urine pregnancy test 8. Effective contraceptive method for female subjects of childbearing potential and for male subjects 9. Able to understand study procedures and attend all study visits 10. Willing to refrain from use of all other systemic or topical agents for the treatment of AD or the prevention of complications of AD (e.g., secondary infection) Exclusion Criteria: 1. Active skin infection and/or systemic infection requiring systemic or topical antimicrobial agents and/or a skin drainage procedure, or a history of recurrent bacterial skin infections 2. Other concurrent skin diseases which could interfere with the diagnosis and/or management of AD (e.g., psoriasis, contact dermatitis), or presence of open, chronic non-healing wounds in their treatable AD lesions 3. Known hypersensitivity to study drug, its excipients, simethicone, and/or any emollient to be used in study 4. Planned treatment with a prohibited medication during study, or received a prohibited medication within time frame noted below, prior to first dose of study drug: Must be discontinued at least 28 Days prior to Day 1: * Systemic corticosteroids * Systemic JAK inhibitors and immunosuppressive agents * Nonbiologic investigational agent or device * Total body phototherapy Must be discontinued at least 14 Days prior to Day 1: * Systemic antimicrobials * Probiotics and prebiotics * Prescription skin barrier repair products Must be discontinued at least 7 Days prior to Day 1: * Topical therapies for AD * Topical antimicrobials and antiseptic cleansers * Use of antibacterial soaps or topical sodium hypochlorite-based products * Current emollient use (need to convert to study emollient 7 days prior to Day 1) 5. Currently being treated with biologic agents; exception: may be enrolled if dupilumab was discontinued at least 12 weeks prior to Day 1, or if other biologics were discontinued at least 5 half-lives prior to Day 1. 6. Female subjects who are pregnant, breastfeeding, or planning a pregnancy, or are of childbearing potential and not using an effective and allowed form of contraception. 7. Enrolled in another investigational study 30 days prior to Screening or 90 days prior to Screening if investigational agent was a phage product. 8. Other medical and/or psychiatric conditions which makes the subject inappropriate for study participation, increases likelihood that the subject will not be able to comply with study therapy or procedures and/or which places the subject at undue risk 9. Active abuse of alcohol and/or illicit drugs or a history of such abuse that would make it difficult for the subject to comply with study and/or place subject at undue risk 10. Known infection with human immunodeficiency virus (HIV) or other immunodeficiency disorder. 11. Current or prior history of a malignant neoplasm other than previously treated non-melanoma skin cancer