Modelling and Simulation of a SIR-type Epidemic with Cellular Automata and Ordinary Differential Equations – Definition ARGESIM Benchmark C17R

Abstract

This Comparison investigates a classical population model for the spread of infection diseases (SIR ordinary differential equations model by Kermack and McKendrick) and an inhomogeneous spatial approach using cellular automata. An identification of parameters based on an abstract time discrete conceptual model is presented. The tasks of this comparison include the validation and analysis of this identification, an investigation on the impact of different spatial dynamics in the cellular automaton modelling approach and simulation scenarios for confining epidemic outbreaks that involve state-dependent interventions.

A Norm-based Comparison of Approaches in ARGESIM Benchmark C17R 'Modelling and Simulation of a SIR-type Epidemic with Cellular Automata and Ordinary Differential Equations' using MATLAB

“…The model was implemented as described in the revised comparison [1] with one exception, which was previously explained resulting in equation 1 for the dimension of the lattice. The initial conditions, represented by the individuals of every population group at time t = 0, were uniformly distributed in the cells of the lattice, which was implemented as a matrix M ∈ N n×n×6 .…”

“…After initializing the LGCA the movement phase is implemented according to the rules, which were defined in the revised comparison [1] and extended by the boundary condition presented in the Introduction.…”

“…This model comparison follows the outlined tasks of the revised ARGESIM Comparison 17 [1] and is targeted on quantifying the difference of SIR-type epidemic simulations, which were either modelled by classical ordinary differential equations (ODEs) or a lattice gas cellular automaton (LGCA). Both modelling approaches use the same system definition and therefore the same basis for parameter calculation.…”

“…Although both models are strictly defined in the re-vised Comparison 17 [1] some changes or specifications had to be made:…”

Modeling and Simulation Using Cellular Automata

“…While CA today are applied in a number of domains, for example fault-tolerant quantum computing (see [25]), image encryption (see [19]), modeling of epidemic spreading (see [17]), and object detection in computer vision (see [21]), this paper takes a closer look at their application in the area of modeling and simulation.…”