You are thinking of an epidemic as a global event, most epidemics are local. The number of infection will spike and they will infect a number of people kill a percent of the population. Once their is not a sufficient amount of people to sustain the epidemic it returns to base level of infection. Eventually it moves to another region or will occur in the same population once conditions are again favourable.
The black death that swept through Europe had this pattern. As have other recent cases of hotspots with SARS, Ebola, Yellow, Denge and others.