Final answer:
A patient with symptoms of delayed umbilical cord separation, recurrent skin and mucosal bacterial infections, and severe periodontal disease most likely suffers from Chronic Granulomatous Disease (CGD), where a defect in the NADPH oxidase system impairs antibacterial activity of phagocytes.
Step-by-step explanation:
A patient with symptoms of delayed umbilical cord separation, recurrent skin and mucosal bacterial infections without purulence, and severe periodontal disease most likely has Chronic Granulomatous Disease (CGD). CGD is caused by defects in the NADPH oxidase system of phagocytic cells like neutrophils and macrophages. These defects prevent the cells from producing superoxide radicals necessary for killing bacteria, leading to infections that can cause chronic inflammation known as granulomas. This disease makes patients especially vulnerable to bacterial infections due to the impaired antibacterial activity of their phagocytes. The severe form of periodontitis seen in these patients is often due to the bacteria that proliferate as a result of the weakened immune system.