A Clinical Study of MK-1045 in People With Lupus or Rheumatoid Arthritis (MK-1045-004)

This study looks at a study medicine called MK-1045 in people with lupus and rheumatoid arthritis (RA). The main goal of the study is to learn about the safety of MK-1045 and if people tolerate it when they receive it at different dose levels (amounts).

Inclusion Criteria: * Has a body mass index between 18 and 32 kg/m\^2, inclusive * Systemic lupus erythematosus (SLE): Has a diagnosis of SLE for at least 6 months and met the European Alliance of Associations for Rheumatology (EULAR)/ American College of Rheumatology (ACR) 2019 classification criteria * SLE: Is taking at least one background therapy for SLE * RA: Has a diagnosis of RA for at least 6 months and meets the 2010 ACR-EULAR classification criteria for RA Exclusion Criteria: * Has a known active infection (excluding fungal infection of nail beds), or any major episode of infection requiring hospitalization or treatment with anti-infectives within 8 weeks prior to the Day 1 dosing * History of serious recurrent or chronic infection * Is known to be infected with hepatitis B virus, hepatitis C virus, or human immunodeficiency virus * Has evidence of active tuberculosis (TB), latent TB, or inadequately treated TB * Has a significant or uncontrolled medical disease in any organ system not related to RA or SLE * For RA participants, has a history of any arthritis with onset before age 17 years * Has a current inflammatory condition other than SLE or RA that could interfere with disease activity assessments * History of cancer (except fully treated nonmelanoma skin cancers or cervical carcinoma in situ after complete surgical removal) and is disease free for \