[Zurück]

M. Bicher, N. Popper:
"Agent-Based Derivation of the SIR - Differential Equations";
in: "EUROSIM 2013 8th EUROSIM Congress on Modelling and Simulation", K. Al-Begain, D. Al Dabass, A. Orsoni, R. Cant, R. Zobel (Hrg.); herausgegeben von: The Institute of Electrical and Electronics Engineers, Inc.,; EUROSIM 2013 8th EUROSIM Congress on Modelling and Simulation, Cardiff, 2013, ISBN: 978-0-7695-5073-2, S. 306 - 311.

Abstract-Due to exponentially increasing computational
resources, individual-based models are getting more and more
popular among epidemiologists. Inspired by SIR (Susceptible-
Infected-Recovered) epidemics very complex and flexible
models for diseases and vaccine strategies can be created
accepting the risk, that maybe unexplained and unpredictable
chaotic group-behavior could distort the results. Preventive
theoretical analysis of these microscopic models is still very
difficult. Based on the idea of diffusion approximation a
technique is presented, how the mean value of a simple
predefined agent-based SIR model can be calculated to
asymptotically satisfy the classic SIR differential equations by
Kermack and McKendrick. This technique can be generalized
to contribute to the analysis of agent-based models and can
help developing hybrid models

Epidemics; Agent-based; Diffusionapproximation; Markov-modelling; Fokker-Planck equation; Kramers-Moyal decomposition