Is a doctor who goes into internal medicine specializing in infectious disease still consider to be a primary care doctor?

Primary care: General internal medicine is one of several primary care specialties. An infectious disease specialist is an internist who has done a fellowship in that sub specialty and usually practices as a consultant, but may also continue to practice general internal medicine

Most : Who specialize in infectious disease focus on this. But they can also be a primary care doctor. So It really depends on the doctors focus in practice

Usually not: He/she is certainly qualified since they did an internal medicine residency. But since they specialized in ID they most likely limit their practice to ID.