What do we call an infectious disease that affects a large number of people within a community at the same time?

An infectious disease that affects a large number of people within a community at the same time is referred to as an epidemic. This term specifically describes situations where the incidence of a disease exceeds what is normally expected within that population or geographical area, indicating a sudden increase in cases.

In contrast, a pandemic refers to an epidemic that has spread over multiple countries or continents, impacting a much wider demographic. An outbreak is a term that can describe a similar situation, but it often pertains to smaller or localized increases in disease cases that may not reach the scale of an epidemic. Endemic signifies a disease or condition that is regularly found and consistently prevalent within a certain geographic area or population but does not imply a surge or increase in cases. Thus, the definition and scope of "epidemic" align precisely with the description provided in the question.