# Test for difference from 0 for non-normal distribution

I'm using an agent based model to study disease transmission. After the initial outbreak, percentage of population infected decreases to zero. I'm looking for a rigorous way to choose when the % infected is not meaningfully different from 0 and can end the simulation.

Clearly there cannot be a negative rate of infection so the distribution of trial outcomes at a certain point in time cannot follow a normal distribution and the variances of different scenarios are different so I don't believe I can use a t-test.

Is there obvious alternatives, the distribution for outcomes generally looks like a poisson where lamba grows smaller and smaller until it becomes 0. My goal is simply to identify the point at which I can say with 95% confidence that lambda is 0.