The period between infection and sporulation of pathogen is known as

The period between infection and sporulation of a pathogen is known as Latent period.
The period from the time of infection to the time of becoming infectious is called the pre-infectious period or the latent period.
The latent period is the time taken by a phage particle to reproduce inside an infected host cell. The infection of disease begins when a pathogenic (disease-causing) infectious agent, or a pathogen, is successfully transmitted from one host to another.