Main Inclusion Criteria:  Men and women aged 18 years or older at screening (V1) Female participants are eligible if they are: i) of non-childbearing potential or ii) of childbearing potential with a negative pregnancy test result at screening and randomization AND agreeing to use a highly effective method of contraception until 72 hours after taking the last study treatment dose. Presence of rosacea, papulopustular phenotype. Moderate or severe rosacea based on Investigator's Global Assessment based on Investigator's judgement. Patients accepting to provide and legally capable of providing free and informed consent to all procedures included in the protocol (including the availability to perform a Lactulose Breath Test).  Main Exclusion Criteria:  Granulomatous rosacea or rosacea fulminans. Hypersensitivity or intolerance to lactulose or any excipient of the lactulose preparation to be used for L-BT. History of inflammatory bowel disease (Crohn's disease or ulcerative colitis) or other conditions characterized by severe intestinal ulcers. Patients with intestinal obstruction or partial intestinal obstruction. Severe kidney impairment (i.e. estimated glomerular filtration rate <30 ml/min). Severe hepatic impairment (i.e. Child-Pugh B or C). Cancer or any cancer-related treatment within 5 years prior to screening (excluding non-melanoma skin-cancer). History of alcohol or drug abuse within a year prior to screening, based on Investigator's judgement. Facial skin conditions that can interfere with reliable assessment of rosacea throughout the study (e.g. facial hair, tattoos, other facial adornments, keloids, hypertrophic scarring, recent facial surgery, excessive sun exposure including use of tanning beds) Any other significant health condition (e.g. cardiovascular, respiratory, renal, hepatic, neurologic, psychiatric, hematologic, oncologic, immune etc.) or non-health condition that in the investigator's judgement may: i) jeopardize the patient's safe participation in the trial or ii) make unlikely the patient's completion of the study or iii) make unlikely the patient's compliance with the study procedures (e.g. highly anticipated need of non-permitted treatments, terminal illness, etc.). History of hypersensitivity to the study drug. Treatment with biologic immunomodulatory and/or immunosuppressive drugs (e.g. anti-TNF drugs) within 6 months prior to randomization. Treatment with non-biologic immunomodulatory and/or immunosuppressive drugs (e.g. cyclosporine, methotrexate etc.) within 30 days prior to randomization. Treatment with warfarin (or other coumarins) within 14 days prior to randomization. Treatment with niacin within 30 days prior to randomization. Topical facial or systemic antibiotics within 30 days before randomization; Treatment with neomycin or other low-absorbable oral antibiotics within 90 days before randomization. Topical facial, inhaled or systemic corticosteroids within 30 days prior to randomization. Topical facial retinoids within 30 days before randomization. Systemic retinoids within 6 months before randomization. Any other topical or systemic treatment for rosacea within 30 days before randomization (including also laser and pulsed light, etc.). Over-the-counter intestinal or topical skin probiotics (functional food is allowed), within 30 days before randomization. Any experimental treatment within 6 months prior to randomization. Current swab-positive or suspected (under investigation) Covid-19 infection; or fever and one or more of the following respiratory disease signs or symptoms: cough, sputum production, shortness of breath within the last 14 days; or contact with people with Covid-19 infection within the last 14 days. Women who are pregnant, breast-feeding or planning a pregnancy during the trial period. Subjects who are investigational site staff members and their family members, site staff members otherwise supervised by the investigator, or patients who are Alfasigma's employees.