Which system most likely interact and cause the severity of infections to vary?

The answer is an immune and endocrine system.

Immune and endocrine system are connected in a complex way. Hormones are specific modulators of immune cell and are able to affect their activation and function. The severity of infection depends on their interaction. For example, testosterone can suppress the immune system. In the case of infection, the body is more susceptible to infection. This can partially explain the fact that autoimmune diseases are more common among the women than men.