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 in one dt, dead_rate*dt is a probability.

The process has two parameters: (i) birth and (ii) dead rates.

Notice however, that birth rate has to be bigger than the dead rate 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 to be the clock. Them, we measure dead rate in units of this clock. This way, particles give birth with probability 1 in one dt unit. At the same time, in this same period, particles can die with a probability 0 < dead_rate = dead/birth <1.