Comparison of a microscopic and a macroscopic age-dependent SIR model

Authored by M Bicher, N Popper, G Schneckenreither

Date Published: 2017

DOI: 10.1080/13873954.2016.1232279

Sponsors: No sponsors listed

Platforms: MATLAB

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

In this work, we compare two structurally different modelling approaches for the simulation of an age-dependent SIR (susceptible, infected, recovered)-type epidemic spread: a microscopic agent-based model and a macroscopic integro-partial differential equation model. Doing so, we put a newly derived mean-field theorem for mixed state-spaces (continuous and discrete) to the test, analytically proving the asymptotic equivalence of the results of both simulations on the aggregate level. Afterwards, both models are executed and compared for abstract scenarios to affirm the derived equivalence. As both models are hereby proven to deliver (asymptotically) the same results, they can be used to supplement each other in terms of structural knowledge of the model, identification and determination of parameters and their values, as well as finally verification and validation.

Tags

Agent-based modelling Dynamics Aggregation Markov process epidemic model Mean-field Lattice Mean-field modelling Mean-field theorem