The Algorithm

The Monte Carlo method implemented by the algorithm start by normalizing rates and then normalizing so to have only one parameter: dead_rate.

So we want that in one dt unit of time, (dead_rate)dt is a probability.

The process has two parameters: (i) birth and (ii) dead rates. Notice however, that birth has to be bigger than dead or the process goes extinct. So, particles must give birth before they die. This means we can take the time it takes to give birth (1/birth) to be the clock of our system (nothing happens faster than this). Now we measure rates in units of this clock. This way, particles give birth with probability birth/birth = 1 in one dt unit. At the same time, in this same period, particles can die with probability dead_rate = dead/birth.