The population of TITAN is maintained as a graph structure containing nodes (agents) and relationships between agents (edges). In the model, an agent class is defined where any given agent maintains its own information within the data structure. These include variables such as the agents age, demographics, partner tree, infection status, or enrollment in treatment programs. A group of agents is defined as an agent set, where agents within the set can be connected or group based on desirable variables, such as the PWID set which contains all PWID agents. These sets allow the population structure to be well organized while not mutually exclusive so as to ease the searching and sorting of the total populations sub-strata.

The model is initialized generating the total N agents which are classified based on input demographic information in a stochastic process, then placing agents in a network space. As the model proceeds in monthly time steps, links are broken and formed between agents, thus representing a dynamic sexual and injecting network. Agents leave the population when they die from infection related or other natural causes, and are replaced in a stochastic manner (i.e., the new agent does not necessarily carry the same traits as the previous agent, but are replaced according to the distributions specified during model initialization). Thus, a constant population size is maintained over the life of the simulation, where each new iteration, or time step, represents an evolution of the population forwards in time.