From Agent Based Infectious Disease Models to Compartment Models

There are lots of potential agent based approaches to COVID modelling, and it is of interest to try to connect them to more standard compartment ODE models. To what extent can any ODE model capture the properties of a given ABM? The Inhomogeneous Random Social Network (IRSN) framework I have developed recently provides an explicit setting where such questions can be explored mathematically. The IRSN approach starts with a finite number N of heterogeneous agents that interact according to \ AB type rules. Under some conditions, one can analyze their large N limit, and under even more conditions, derive a limiting standard stratified compartment ODE model. The IRSN framework can be made arbitrarily fine-grained in many dimensions, including demographic classification, immunology (multiple variants), contact settings (types of contact locations) but only certain combinations of features are relevant to the ODE limit. ABMs capture characteristics such as non-homogeneous mixing that are not easily captured in any ODE model, so they help to understand the impact of such characteristics on disease propagation.

IRSN Model Paper: https://www.sciencedirect.com/science/article/pii/S2468042720300713

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