A continuous time evolution of a synthetic population

In the last decades we observed an increase in the use of microsimulations to tackle real life problems. In all the applications, different models are applied on top of a synthetic static populations. An even more demanding task is to let such static populations to evolve in time.
Scholars are faced with the problem of many processes each one evolving with its own time scale, for this reason a commonly used approach is to set a time step of one year and execute the processes all at the same time. Despite the good results of this method, it has two flaws: the outcome strongly depends on the order of the processes; and it impossible to deal with phenomena evolving on short time scales. The goal of our work is to propose a method to evolve a synthetic population solving both issues.
The idea is that there is not an a priori fixed order for the processes and the time scale evolves thus continuously. The evolution scheme computes, using a Gillespie algorithm, the most probable time τ at which the change will arise and determines which process among the potential ones to apply. We then obtain a snapshot of the new population at time t + τ and we iterate up to a final time horizon. This evolution scheme is illustrated in Figure 1.
The method can be used with individual agents, in the spirit of agent-based modelling, as well as for agents aggregated in classes, i.e. sharing some common feature. We provide two simple but relevant applications of the method. Being the scheme order-free it can be used to benchmark the commonly used methods based on a a priori fixed order for the processes and check which order configuration provides the most accurate evolution. Second, we can consider processes whose transition probability depends on time, e.g. using some seasonal periodicity, and compare the difference in the outcomes with respect the traditional models with a fixed time scale.