Quite generally, a natural system can be seen as a system that can access a number
of discrete states at rates depending on the state of the system. In this situations, event driven simulations based on Gillespie algorithm provide an exact implementation for the temporal evolution of such a system as a stochastic process in continous time.
Such stochastic processess are well studied and this have a number of advantages.

In particular, one important advantage of these models over discrete-time simulations is that they map perfectly onto differential equations. For example, say you’re starting with a basic SIR (Susceptible-Infected-Recovered) model of disease spreading. Assuming a well mixed system, you can set up a set of differential equations relating the rates of change of the three classes to the densities of the other three classes alone. If you want to relax the assumption of well-mixedness, start by setting up a Gillespie-type model with a fully connected network, so that any individual can be infected by any other individual, with rates proportional to the coefficients in the ODEs. Assuming proper scaling and all that, if you run the model a bunch of times and average the runs, the graph should look exactly like the ODE’s. So you can check your model against the ODE first, and then begin changing assumptions (like the network structure).