Study to Evaluate the Safety, Tolerability, and Pharmacokinetics of Single and Repeat Topical Administration of BOS-475 in Healthy Subjects and Patients With Psoriasis

Inclusion Criteria: Part A * Healthy male or female participants 18 to 65 years of age inclusive, at the time of signing the informed consent. * Male participants must agree to use contraception as detailed in the protocol during the treatment period and for at least 90 days (a spermatogenesis cycle) after the last dose of study drug and refrain from donating sperm during this period. o Male participants who have had a vasectomy with documentation of azoospermia are not required to use contraception. * Female participants must be of non-child bearing potential, defined as 1) at least 12 months of spontaneous amenorrhea with follicle stimulating hormone (FSH) \> 40 milliInternational Units per milliliter (mIU/ml), or 2) having a documented tubal ligation at least 6 weeks prior to dosing; or 3) having had a surgical bilateral oophorectomy (with or without hysterectomy). * Participants who are healthy as determined by the Investigator or medically qualified designee based on a medical evaluation including medical history, physical examination, laboratory tests, and cardiac monitoring. * Participants with body mass index (BMI) within the range 18 to 30 kilograms per meters squared (kg/m\^2) (inclusive). * Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the Informed Consent Form (ICF) and in this protocol * Willing to refrain from using any topical treatments, other than those mandated by the protocol or for protocol procedures Part B * Male or female participants with mild to moderate psoriasis 18 to 65 years of age inclusive, at the time of signing the informed consent * Male participant must agree to use contraception as detailed in the protocol during the treatment period and for at least 90 days (a spermatogenesis cycle) after the last dose of study drug and refrain from donating sperm during this period. o Male participants who have had a vasectomy with documentation of azoospermia are not required to use contraception. * Female of non-child bearing potential is defined as 1) at least 12 months of spontaneous amenorrhea with FSH \> 40 mIU/mL, or 2) having a documented tubal ligation at least 6 weeks prior to dosing; or 3) having had a surgical bilateral oophorectomy (with or without hysterectomy). * Participants who have a clinical diagnosis of stable plaque psoriasis for ≥ 6 months, as confirmed by the Investigator * A Psoriasis Physician Global Assessment (PGA) score of ≥ 2 at screening and Day 1 * At least 1 psoriasis plaque located on the trunk or extremities (excluding knees and elbows) that is at least 5 centimeters squared (cm\^2) in size at Screening and Day 1 with a Target Plaque Severity Score (TPSS) ≥ 5 and induration subscore ≥ 2 * Body Surface Area (BSA) involvement of psoriasis lesions between 2% and 15%, excluding face, scalp, palms, soles, nails, and intertriginous areas at screening * Participants with BMI within the range 18 to 35 kg/m\^2 (inclusive) * Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the ICF and in this protocol * Willing to refrain from using any topical treatments, other than those mandated by the protocol or for protocol procedures Exclusion Criteria: * History or presence of cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological, neurological, or skin disorders, in the Investigator's opinion, may significantly alter the absorption, metabolism, or elimination of drugs; constituting a risk when taking the study treatment; or interfering with the interpretation of data * Current evidence of any acute cutaneous infection, history of repeated or chronic significant skin infections (unless irrelevant in the opinion of the Investigator, i.e., onychomycosis, labial herpes or other minor diagnosis) * Women of child-bearing potential, is pregnant, or is breastfeeding * Known history of chronic hepatitis or human immunodeficiency virus (HIV); positive findings of hepatitis B surface antigen or hepatitis C virus (HCV) antibody associated with a positive HCV ribonucleic acid (RNA) polymerase chain reaction; or positive HIV screening test suggesting active disease at the screening visit * Current or chronic history of liver disease, or known hepatic or biliary abnormalities (with the exception of Gilbert's syndrome or asymptomatic gallstones) * Abnormal blood pressure, liver, or renal function * History of malignancy within 5 years prior to dosing, except adequately treated non-invasive skin cancer (basal or squamous cell carcinoma) * History of hypersensitivity to any of the study treatments, or components thereof, or drug or other allergy that, in the opinion of the Investigator or medical monitor, contraindicates participation in the study * For Part A only: psoriasis of any kind (i.e., plaque, acute psoriasis guttate, psoriasis punctata, psoriasis erythroderma, or pustular psoriasis) * For Part A only: any clinically-relevant skin disease or other skin pathologies, that may, in the opinion of the Investigator, contraindicate participation or interfere with skin evaluations * For Part A only: history or risk of complications from skin biopsy including impaired wound healing, excess bleeding, infection, or scarring/keloid formation or known hypersensitivity to local anesthetics. Use of anticoagulant medication. * Use of prohibited concomitant medications or natural products within the defined periods before the Day 1 visit and during the trial * Current heavy smoker (those who smoke ≥ 25 cigarettes a day) or former heavy smoker who has stopped smoking within 1 month prior to screening * Positive urine drug or alcohol test results during screening, or at Day 1, or history of drug abuse within a year prior to the screening visit * Excess alcohol consumption within 6 months prior to the study defined as an average weekly intake of \> 14 units for males and females. One unit is equivalent to 8 grams of alcohol: a half-pint (\~240 mL) of beer, 1 glass (125 mL) of wine, or 1 (25 mL) measure of spirits * Donation or significant loss of blood within 3 months prior to screening, or plasma up to 14 days prior to screening * Participation in any clinical research study within 30 days or 5 half-lives, of the investigational product, whichever is greater, prior to the screening visit