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

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. Introduction 1 System Definition Parameter Description initial number of susceptible initial number of infected initial number of recovered contacts infection probability recovery probability Table 1. System parameters. Miksch et al. SIR-type Epidemics: ODEs vs CAs – Definition Benchmark C17R 50 SNE 25(1) – 4/2015 BN • • • Interventions. Figure 1. Illustration of a ‘soft’ intervention. Once the number of infected reaches a critical threshold, the infection parameter decreases over a certain period of time. Parameter Description Fraction that defines the threshold Reduction parameter of a soft intervention Duration of a soft intervention Fraction parameter of a hard intervention Table 2. Parameter of hard and soft interventions. 2 Differential Equations Model Miksch et al. SIR-type Epidemics: ODEs vs CAs – Definition Benchmark C17R SNE 25(1) – 4/2015 51 B N Parameter Identification Table 3. Parameter identification of the differential equation model. Interventions. 3 Cellular Automaton Model Miksch et al. SIR-type Epidemics: ODEs vs CAs – Definition Benchmark C17R 52 SNE 25(1) – 4/2015 BN • • Figure 2. Schematic visualization of LGCA movement rules. Figure 3. FHP-I collision rules. Parameter Identification Table 4. Parameter identification of the cellular automaton model. Interventions. Miksch et al. SIR-type Epidemics: ODEs vs CAs – Definition Benchmark C17R SNE 25(1) – 4/2015 53 B N 4 Analytical Comparison Infections Recoveries