A Study of Baricitinib (LY3009104) in Adult and Pediatric Japanese Participants With NNS/CANDLE, SAVI, and AGS

Inclusion Criteria: * Have systemic signs and symptoms of inflammation as manifested NNS/CANDLE, SAVI, AGS * Have been diagnosed with genetic diagnosis * Men must agree to use a reliable method of birth control during the study * Women not of child-bearing potential or nonbreastfeeding * Women must agree to use birth control or remain abstinent during the study and for at least 12 weeks after stopping treatment * NNS/CANDLE and SAVI patients who are ≥17.5 months of age * AGS patients who are ≥6 months of age * Are ≥ 5kg in body weight Exclusion Criteria: * Have received immunosuppressive biologic agent/monoclonal antibody/oral JAK inhibitor/OAT3 inhibitor and cannot discontinue prior to investigational product initiation. Note: A washout period is required to each drug. * Have diagnosis of current active tuberculosis (TB) or, latent TB who did not receive appropriate treatment. * Have had a serious infection within 12 weeks prior to screening. * Have a history of lymphoproliferative disease * Have any history of venous thromboembolic event (VTE) (deep vein thrombosis \[DVT\]/pulmonary embolism \[PE\]) prior to screening. * Have had any major surgery within 8 weeks prior to screening. * Have previously been enrolled in any other study investigating baricitinib.