The general approach in the simulation is as follows:

For a given time interval dt and total US population N (~ 300 million people - this value is updated as the simulation progresses), calculate the expected number of births or deaths in the interval as

λ = (birth or death rate per year per 1000) * (N/1000) * dt

Estimate the number of births or deaths for the interval as a sample from a Poisson distribution with mean of λ calculated from previous step.

For each birth or death obtained this way, determine in which county it occurred by calculating a random number and then choosing the county based on its fraction of the total population (e.g., if a county has 0.001% of the total population, then there is a 0.001% chance that this county would be the one where it occurred). Once the county is determined, a similar process is used to determine which city/town this event occurred in the county (or outside of any city/town in in the county, which can happen).
AuthorSheffield Leithart