Yeah no worries. I was confused why you were looking for other things and did see that you had tried it with an error haha. My inner voice was “what the heck is this guy asking for?”
But yeah, getting “exact” extinctions in an ODE-based model is always hard. ODEs generally don’t go extinct: it’s a downside to that modeling choice. If you want that kind of behavior, continuous-time Markov chains are where people go. Catalyst.jl is made for that.
https://catalyst.sciml.ai/dev/
Though then the results are stochastic and require more time to interpret.