Calculate transition probabilities using monte carlo simulations.

I am developing a Markov Chain Model for discrete time and discrete states. I want to determine the transition probabilities using "already estimated transition rates". I will calculate these probabilities using monte carlo simulations. So I will first project the life profiles of a "virtual population" and then would randomly let them make transitions. for example, for a person who is in state = single at time t, there are two possible states in the next period marriage and death with some predicted probability "p", then I generate random numbers and compare them with 'p' and if 'p' is higher than random draw then the individual make the transition otherwise he remains single. (I assume here that 'p' is the transition rate). once simulations are done, i will determine the "transition probabilities", which is the aim of performing this step.

when I run these monte carlo simulations, I also need to keep the track of "event histories of simulated population" like how longer the person remained divorced or married?

My question is how do can we keep track of "event history" of the simulated population over time t in MATLAB?

Secondly, if someone has already worked in this area, please share any useful tips.

Thank you in advance.