# Condition for a genetically modified group of cell to remain and to spread?

I was wondering: when a treatment modifies a group of gene (like in gene therapy), what makes a group of cell remains?

I mean, when a cell divide itself to create new ones, if a cell was initially genetically modified, it will lead to two modified one, right? But, I assume that we have a finite number of cells in our body, so if the process was going on like that, we would just have to modify one cell of our body. But, besides this, the other cells divide themselves too, so there might be something that makes a group of cell dominant (like the proportion, the number of neighbors of one cell...).

So, my question (cut in three) is:

• What are the conditions for a group of modified cells to remain?
• In what extend the modification can spread?
• If it can't spread, why?

(I'm not a biologist student (I studied it in high school, so I may be able to understand the basics), but I'm interested in making a mathematical model of such a process. So if there is an answer, could you make it understandable for someone who has only the basis?)