Models of community growth

The academic literature often proposes simple models that help us think about the behavior of a system. For instance, the Bass Diffusion Model is a famous mathematical model that captures the dynamics of new product adoption.

What are some of the most popular / widely used models of community growth that have been studied in the academic literature? I’m especially interested in simple models that capture the impact of key characteristics like the current size of the community, the size of the overall population that might be interested in the community, and the visibility of the community to the overall population.