Agent-based models (ABMs) are powerful in describing structured epidemiological processes involving human behavior and local interaction. The joint behavior of the agents can be very complex and tracking the behavior requires a disciplined approach. At the same time, equationbased models (EBMs) can be more tractable and allow for at least partial analytical insight. However, inadequate representation of the detailed population structure can lead to spurious results, especially when the epidemic process is beginning and individual variation is critical. In this paper, we demonstrate an approach that combines the two modeling paradigms and introduces a hybrid model that starts as agent-based and switches to equation-based after the number of infected individuals is large enough to support a population-averaged approach. This hybrid model can dramatically save computational times and, more fundamentally, allows for the mathematical analysis of emerging structures generated by the ABM.
Choosing an appropriate formalism for an epidemiological model can pose a challenge. The type of description can range from a compartmental model to very detailed ABMs defined by contact networks (Riley, 2007). Some back-to-back comparison of equation-based and agentbased models of dynamics of contagion was done in Rahmandad and Sterman (2007). Equation-based approaches, such as compartmental models, operate on global laws defined by the equations and apply to all members of the compartment. Adding stochasticity does not change the description in principle, but rather utilizes the concept of independent and identically distributed (iid) objects. In a number of situations such as the spread of infectious diseases, especially sexually transmitted diseases, it is important to describe more detailed microlevel transmission processes.