# Agent-Based Simulation for Infectious Disease Modelling over a Period of Multiple Days, with Application to an Airport Scenario

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- almost arbitrarily applicable to scenarios defined by a two-dimensional floor-plan
- capable of handling large areas and high agent counts
- incorporates a basic model of aerosol spreading
- augmented by extending the time span over multiple days to account for the temporal progress of infection dynamics

## 2. Related Work

## 3. Materials and Methods

#### 3.1. Pedestrian Dynamics

#### 3.2. Simulation Domain Modelling and Pathfinding

#### 3.3. Pedestrian Simulation

#### 3.4. Infectious Disease Modelling

#### 3.4.1. Aerosol Modelling

#### 3.4.2. Extension and Coherence over Multiple Days

Name | Description |
---|---|

a | Model parameter |

$\widehat{a}$ | Model parameter (A in [4]) |

b | Model parameter |

$\widehat{b}$ | Model parameter (B in [4]) |

${c}_{i}$ | Infectivity of ${p}_{i}$ |

${c}_{i}^{\mathrm{vt}}$ | Virus-variant of ${p}_{i}$ |

${c}_{i}^{\mathrm{ae}}$ | Tidal air virus load of ${p}_{i}$ |

${c}_{i}^{\mathrm{aexp}}$ | Aerosol exposure level of ${p}_{i}$ |

${c}_{vt}^{\mathrm{crit}}$ | Necessary viral load for infection per variant |

${d}_{i}^{\mathrm{inc}}$ | Incubation time for ${p}_{i}$ |

${d}_{\mathbf{w}}$ | Distance to wall |

${\mathbf{d}}_{i},{\mathbf{d}}_{k}$ | Destination point |

D | Set of all way- and destination points |

${D}_{D}$ | Set of all destination points |

${D}_{W}$ | Set of all waypoints |

${\mathbf{e}}_{ij}$ | Direction from ${p}_{i}$ to ${p}_{j}$ |

${\mathbf{f}}_{i}^{0}$ | Self-acceleration |

${\mathbf{f}}_{ij}$ | Agent-to-agent force |

${\mathbf{f}}_{i}^{\mathrm{wall}}$ | Wall force |

$\mathbf{F}$ | Binary floor map |

${\mathbf{G}}_{k}^{\mathrm{dir}}$ | Direction map for ${\mathbf{d}}_{k}$ |

h | Height of simulated area in metres |

${h}_{F}$ | Height of floorplan in pixels |

$\widehat{k}$ | Model parameter (K in [4]) |

${m}_{\mathrm{total}}$ | Number of simulated days |

${\mathbf{n}}_{ij}$ | Vector perpendicular to ${\mathbf{t}}_{ij}$ |

${\mathbf{n}}_{\mathbf{w}}$ | Wall normal |

n | Number of agents |

${n}_{P}$ | Size of agent pool |

${n}^{\prime}$ | Model parameter |

$\Omega $ | Simulation area |

${\varphi}^{\mathrm{ae}}$ | Map of aerosol concentration |

${\varphi}^{\mathrm{dt}}$ | Distance transform of $\mathbf{F}$ |

${\varphi}^{\mathbf{F}}$ | Floor-plan/obstacle map |

${p}_{i}$ | Agent |

${p}_{i}^{\mathrm{pst}}$ | Persistent agent |

${P}_{\mathrm{sim}}$ | Set of simulated agents |

${P}_{\mathrm{pool}}$ | Set of all available agents |

${P}_{\mathrm{persist}}$ | Set of persistent agents |

${r}_{\mathrm{ae}}$ | Radius of aerosol distribution in metres |

${r}_{\mathrm{resp}}$ | Respiration rate |

${\mathbf{s}}_{i}$ | Starting point of agent ${p}_{i}$ |

S | Set of all starting points |

${\mathbf{s}}_{k}$ | Starting point |

${\mathbf{t}}_{ij}$ | Interaction direction between ${p}_{i}$ and ${p}_{j}$ |

${t}_{0}$ | Time of simulation start |

${t}_{\mathrm{max}}$ | Time of simulation end |

${t}_{\mathrm{frame}}$ | Length of time-frame for aerosol calculation |

${t}_{\mathrm{steps}}$ | Sampling rate for time-frames |

$\tau $ | Relaxation constant |

${\mathbf{v}}_{i}$ | Velocity of ${p}_{i}$ |

${v}_{i}^{0}$ | Desired speed of ${p}_{i}$ |

$\mathbf{w}$ | Wall/obstacle position |

W | The set of all obstacle positions |

w | Width of the simulated area in metres |

${w}_{F}$ | Width of floor-plan in pixels |

${\mathbf{x}}_{i}$ | Position of ${p}_{i}$ |

## 4. Experiments

## 5. Results

#### 5.1. Single Virus-Variant

#### 5.2. Two Virus-Variants

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABM | Agent-Based Model |

CFD | Computational Fluid Dynamics |

COVID-19 | Corona Virus Disease 2019 |

CPU | Central Processing Unit |

GIS | Geographic Information System |

GPU | Graphics Processing Unit |

IBM | Individual-Based Model |

ICTV | International Committee on Taxonomy of Viruses |

mRNA | Messenger Ribonucleic Acid |

OpenMP | Open Multi-Processing |

OpenCL | Open Computing Language |

RNA | Ribonucleic Acid |

SARS-CoV-2 | Severe Acute Respiratory Syndrome CoronaVirus 2 |

SEIR | Susceptible–Exposed–Infectious–Recovered |

SIIRD | Susceptible–Infected asymptomatic–Infected symptomatic–Recovered–Dead |

SIR | Susceptible–Infected–Removed |

SIRD | Susceptible–Infected–Recovered–Deceased |

+ssRNA | Positive-sense single-stranded RNA |

SVIR | Susceptible–Vaccinated–Infected–Removed |

WHO | World Health Organization |

US | United States |

UK | United Kingdom |

## References

- Ucler, C.; Martin-domingo, L. Traveler’s idle time and the value chain at airports. J. Aeronaut. Space Technol. (Havacilik Ve Uzay Teknol. Dergisi)
**2015**, 8, 13. [Google Scholar] [CrossRef] - Zhu, N.; Zhang, D.; Wang, W.; Li, X.; Yang, B.; Song, J.; Zhao, X.; Huang, B.; Shi, W.; Lu, R.; et al. A Novel Coronavirus from Patients with Pneumonia in China, 2019. N. Engl. J. Med.
**2020**, 382, 727–733. [Google Scholar] [CrossRef] - Sirkeci, I.; Yüceşahin, M. Coronavirus and Migration: Analysis of Human Mobility and the Spread of COVID-19. Migr. Lett.
**2020**, 17, 379–398. [Google Scholar] [CrossRef] [Green Version] - Moussaïd, M.; Helbing, D.; Garnier, S.; Johansson, A.; Combe, M.; Theraulaz, G. Experimental study of the behavioural mechanisms underlying self-organization in human crowds. Proc. R. Soc. B Biol. Sci.
**2009**, 276, 2755–2762. [Google Scholar] [CrossRef] [Green Version] - Harweg, T.; Bachmann, D.; Weichert, F. Agent-based simulation of pedestrian dynamics for exposure time estimation in epidemic risk assessment. J. Public Health
**2021**, 1–8. [Google Scholar] [CrossRef] - Brauer, F. Compartmental Models in Epidemiology. In Mathematical Epidemiology; Brauer, F., van den Driessche, P., Wu, J., Eds.; Springer: Berlin/Heidelberg, Germany, 2008; pp. 19–79. [Google Scholar] [CrossRef]
- Nepomuceno, E.; Resende, D.; Lacerda, M. A Survey of the Individual-Based Model applied in Biomedical and Epidemiology Research. J. Biomed. Res. Rev.
**2018**, 1, 11–24. [Google Scholar] [CrossRef] - Garcia, W.; Mendez, S.; Fray, B.; Nicolas, A. Model-based assessment of the risks of viral transmission in non-confined crowds. Saf. Sci.
**2021**, 144, 105453. [Google Scholar] [CrossRef] - Parisi, D.R.; Patterson, G.A.; Pagni, L.; Osimani, A.; Bacigalupo, T.; Godfrid, J.; Bergagna, F.M.; Rodriguez Brizi, M.; Momesso, P.; Gomez, F.L.; et al. Physical distance characterization using pedestrian dynamics simulation. Pap. Phys.
**2022**, 14, 140001. [Google Scholar] [CrossRef] - Mayr, C.M.; Köster, G. Social Distancing with the Optimal Steps Model. Collect. Dyn.
**2021**, 6, 1–24. [Google Scholar] [CrossRef] - Iftekhar, E.N.; Priesemann, V.; Balling, R.; Bauer, S.; Beutels, P.; Calero Valdez, A.; Cuschieri, S.; Czypionka, T.; Dumpis, U.; Glaab, E.; et al. A look into the future of the COVID-19 pandemic in Europe: An expert consultation. Lancet Reg. Health-Eur.
**2021**, 8, 100185. [Google Scholar] [CrossRef] - Gao, X.; Li, Y.; Leung, G.M. Ventilation Control of Indoor Transmission of Airborne Diseases in an Urban Community. Indoor Built Environ.
**2009**, 18, 205–218. [Google Scholar] [CrossRef] - Noakes, C.J.; Beggs, C.B.; Sleigh, P.A.; Kerr, K.G. Modelling the transmission of airborne infections in enclosed spaces. Epidemiol. Infect.
**2006**, 134, 1082–1091. [Google Scholar] [CrossRef] - Wells, W.F. Airborne Contagion and Air Hygiene: An Ecological Study of Droplet Infections; Commonwealth Fund: Cambridge, MA, USA, 1955. [Google Scholar]
- Riley, E.C.; Murphy, G.; Riley, R.L. Airborne spread of measles in a suburban elementary school. Am. J. Epidemiol.
**1978**, 107, 421–432. [Google Scholar] [CrossRef] - Lazebnik, T.; Bunimovich-Mendrazitsky, S. Generic approach for mathematical model of multi-strain pandemics. PLoS ONE
**2022**, 17, e0260683. [Google Scholar] [CrossRef] - Lazebnik, T.; Bunimovich-Mendrazitsky, S.; Shami, L. Pandemic management by a spatio–temporal mathematical model. Int. J. Nonlinear Sci. Numer. Simul.
**2021**, 000010151520210063. [Google Scholar] [CrossRef] - Fudolig, M.; Howard, R. The local stability of a modified multi-strain SIR model for emerging viral strains. PLoS ONE
**2020**, 15, e0243408. [Google Scholar] [CrossRef] - Khyar, O.; Allali, K. Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: Application to COVID-19 pandemic. Nonlinear Dyn.
**2020**, 102, 489–509. [Google Scholar] [CrossRef] - Arruda, E.F.; Das, S.S.; Dias, C.M.; Pastore, D.H. Modelling and optimal control of multi strain epidemics, with application to COVID-19. PLoS ONE
**2021**, 16, e0257512. [Google Scholar] [CrossRef] - Yagan, O.; Sridhar, A.; Eletreby, R.; Levin, S.; Plotkin, J.B.; Poor, H.V. Modeling and Analysis of the Spread of COVID-19 under a Multiple-Strain Model with Mutations. Harv. Data Sci. Rev.
**2021**. Available online: https://hdsr.mitpress.mit.edu/pub/2q9jiymv (accessed on 8 December 2022). [CrossRef] - Eletreby, R.; Zhuang, Y.; Carley, K.M.; Yağan, O.; Poor, H.V. The effects of evolutionary adaptations on spreading processes in complex networks. Proc. Natl. Acad. Sci. USA
**2020**, 117, 5664–5670. [Google Scholar] [CrossRef] [Green Version] - de León, U.A.P.; Avila-Vales, E.; lin Huang, K. Modeling COVID-19 dynamic using a two-strain model with vaccination. Chaos Solitons Fractals
**2022**, 157, 111927. [Google Scholar] [CrossRef] - Hoertel, N.; Blachier, M.; Blanco, C.; Olfson, M.; Massetti, M.; Rico, M.S.; Limosin, F.; Leleu, H. A stochastic agent-based model of the SARS-CoV-2 epidemic in France. Nat. Med.
**2020**, 26, 1417–1421. [Google Scholar] [CrossRef] - Perez, L.; Dragicevic, S. An agent-based approach for modeling dynamics of contagious disease spread. Int. J. Health Geogr.
**2009**, 8, 50. [Google Scholar] [CrossRef] [Green Version] - Venkatramanan, S.; Lewis, B.; Chen, J.; Higdon, D.; Vullikanti, A.; Marathe, M. Using data-driven agent-based models for forecasting emerging infectious diseases. Epidemics
**2018**, 22, 43–49. [Google Scholar] [CrossRef] - Wang, Y.; Xiong, H.; Liu, S.; Jung, A.; Stone, T.; Chukoskie, L. Simulation Agent-Based Model to Demonstrate the Transmission of COVID-19 and Effectiveness of Different Public Health Strategies. Front. Comput. Sci.
**2021**, 3, 82. [Google Scholar] [CrossRef] - Giacopelli, G. A Full-Scale Agent-Based Model to Hypothetically Explore the Impact of Lockdown, Social Distancing, and Vaccination during the COVID-19 Pandemic in Lombardy, Italy: Model Development. JMIRx Med.
**2021**, 2, e24630. [Google Scholar] [CrossRef] - Müller, S.A.; Balmer, M.; Charlton, W.; Ewert, R.; Neumann, A.; Rakow, C.; Schlenther, T.; Nagel, K. Predicting the effects of COVID-19 related interventions in urban settings by combining activity-based modelling, agent-based simulation, and mobile phone data. PLoS ONE
**2021**, 16, e0259037. [Google Scholar] [CrossRef] - Wolfram, C. An Agent-Based Model of COVID-19. Complex Syst.
**2020**, 29, 87–105. [Google Scholar] [CrossRef] - Ying, F.; O’Clery, N. Modelling COVID-19 transmission in supermarkets using an agent-based model. PLoS ONE
**2021**, 16, e0249821. [Google Scholar] [CrossRef] - Kerr, C.C.; Stuart, R.M.; Mistry, D.; Abeysuriya, R.G.; Rosenfeld, K.; Hart, G.R.; Núñez, R.C.; Cohen, J.A.; Selvaraj, P.; Hagedorn, B.; et al. Covasim: An agent-based model of COVID-19 dynamics and interventions. PLoS Comput. Biol.
**2021**, 17, e1009149. [Google Scholar] [CrossRef] - Krivorotko, O.; Sosnovskaia, M.; Vashchenko, I.; Kerr, C.; Lesnic, D. Agent-based modeling of COVID-19 outbreaks for New York state and UK: Parameter identification algorithm. Infect. Dis. Model.
**2022**, 7, 30–44. [Google Scholar] [CrossRef] - Truszkowska, A.; Behring, B.; Hasanyan, J.; Zino, L.; Butail, S.; Caroppo, E.; Jiang, Z.P.; Rizzo, A.; Porfiri, M. High-Resolution Agent-Based Modeling of COVID-19 Spreading in a Small Town. Adv. Theory Simul.
**2021**, 4, 2000277. [Google Scholar] [CrossRef] - Shamil, M.S.; Farheen, F.; Ibtehaz, N.; Khan, I.M.; Rahman, M.S. An Agent-Based Modeling of COVID-19: Validation, Analysis, and Recommendations. Cogn. Comput.
**2021**, 1–12. [Google Scholar] [CrossRef] - Chumachenko, D.; Dobriak, V.; Mazorchuk, M.; Meniailov, I.; Bazilevych, K. On agent-based approach to influenza and acute respiratory virus infection simulation. In Proceedings of the 2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET), Lviv-Slavske, Ukraine, 20–24 February 2018; pp. 192–195. [Google Scholar] [CrossRef]
- Alvarez Castro, D.; Ford, A. 3D Agent-Based Model of Pedestrian Movements for Simulating COVID-19 Transmission in University Students. ISPRS Int. J. Geo-Inf.
**2021**, 10, 509. [Google Scholar] [CrossRef] - Islam, M.T.; Jain, S.; Chen, Y.; Chowdhury, B.D.B.; Son, Y.J. An Agent-Based Simulation Model to Evaluate Contacts, Layout, and Policies in Entrance, Exit, and Seating in Indoor Activities Under a Pandemic Situation. IEEE Trans. Autom. Sci. Eng.
**2022**, 19, 603–619. [Google Scholar] [CrossRef] - Espitia, E.; Gorrini, A.; Vacca, A.; Deponte, D.; Sarvi, M. How COVID-19 is Affecting Pedestrian Modeling and Simulation: The Case of Venice. Transp. Res. Rec.
**2022**, 03611981221088224. [Google Scholar] [CrossRef] - Alam, M.J.; Habib, M.A.; Holmes, D. Pedestrian movement simulation for an airport considering social distancing strategy. Transp. Res. Interdiscip. Perspect.
**2022**, 13, 100527. [Google Scholar] [CrossRef] - Cuevas, E. An agent-based model to evaluate the COVID-19 transmission risks in facilities. Comput. Biol. Med.
**2020**, 121, 103827. [Google Scholar] [CrossRef] - Nikoohemat, S.; Godoy, P.; Valkhoff, N.; Wouters van Leeuwen, M.; Voûte, R.; Lehtola, V.V. Point cloud based 3D models for agent based simulations in social distancing and evacuation. ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci.
**2021**, 4, 113–120. [Google Scholar] [CrossRef] - Kramer, K.B.; Wang, G.J. Social distancing slows down steady dynamics in pedestrian flows. Phys. Fluids
**2021**, 33, 103318. [Google Scholar] [CrossRef] - Borgefors, G. Distance Transfomations in Digital Images. Comput. Vis. Graph. Image Process.
**1986**, 34, 344–371. [Google Scholar] [CrossRef] - Felzenszwalb, P.F.; Huttenlocher, D.P. Distance Transforms of Sampled Functions. Theory Comput.
**2012**, 8, 415–428. [Google Scholar] [CrossRef] - Dijkstra, E.W. A Note on Two Problems in Connexion with Graphs. Numer. Math.
**1959**, 1, 269–271. [Google Scholar] [CrossRef] [Green Version] - Hart, P.E.; Nilsson, N.J.; Raphael, B. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Trans. Syst. Sci. Cybern.
**1968**, 4, 100–107. [Google Scholar] [CrossRef] - Sethian, J.A. A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. USA
**1996**, 93, 1591–1595. [Google Scholar] [CrossRef] [Green Version] - Valero-Gomez, A.; Gómez, J.; Garrido, S.; Moreno, L. Fast Marching Methods in Path Planning. IEEE Robot. Autom. Mag.
**2013**, 20, 111–120. [Google Scholar] [CrossRef] [Green Version] - Lelieveld, J.; Helleis, F.; Borrmann, S.; Cheng, Y.; Drewnick, F.; Haug, G.; Klimach, T.; Sciare, J.; Su, H.; Pöschl, U. Model Calculations of Aerosol Transmission and Infection Risk of COVID-19 in Indoor Environments. Int. J. Environ. Res. Public Health
**2020**, 17, 8114. [Google Scholar] [CrossRef] - Backer, J.A.; Eggink, D.; Andeweg, S.P.; Veldhuijzen, I.K.; van Maarseveen, N.; Vermaas, K.; Vlaemynck, B.; Schepers, R.; van den Hof, S.; Reusken, C.B.; et al. Shorter serial intervals in SARS-CoV-2 cases with Omicron BA.1 variant compared with Delta variant, the Netherlands, 13 to 26 December 2021. Euro Surveill. Bull. Eur. Sur Les Mal. Transm.—Eur. Commun. Dis. Bull.
**2022**, 27, 2200042. [Google Scholar] [CrossRef] - Cortés Martínez, J.; Pak, D.; Abelenda-Alonso, G.; Langohr, K.; Ning, J.; Rombauts, A.; Colom, M.; Shen, Y.; Gómez Melis, G. SARS-CoV-2 incubation period according to vaccination status during the fifth COVID-19 wave in a tertiary-care center in Spain: A cohort study. BMC Infect. Dis.
**2022**, 22, 828. [Google Scholar] [CrossRef] - Wu, Y.; Kang, L.; Guo, Z.; Liu, J.; Liu, M.; Liang, W. Incubation Period of COVID-19 Caused by Unique SARS-CoV-2 Strains: A Systematic Review and Meta-analysis. JAMA Netw. Open
**2022**, 5, e2228008. [Google Scholar] [CrossRef] - Chen, W.; Zhang, N.; Wei, J.; Yen, H.L.; Li, Y. Short-range airborne route dominates exposure of respiratory infection during close contact. Build. Environ.
**2020**, 176, 106859. [Google Scholar] [CrossRef] - Bogoch, I.I.; Watts, A.; Thomas-Bachli, A.; Huber, C.; Kraemer, M.U.G.; Khan, K. Pneumonia of unknown aetiology in Wuhan, China: Potential for international spread via commercial air travel. J. Travel Med.
**2020**, 27, taaa008. [Google Scholar] [CrossRef] [PubMed] - Sarhan, A.R.; Naser, P.; Naser, J. COVID-19 aerodynamic evaluation of social distancing in indoor environments, a numerical study. J. Environ. Health Sci. Eng.
**2021**, 19, 1969–1978. [Google Scholar] [CrossRef] [PubMed] - Liu, H.; He, S.; Shen, L.; Hong, J. Simulation-based study of COVID-19 outbreak associated with air-conditioning in a restaurant. Phys. Fluids
**2021**, 33, 023301. [Google Scholar] [CrossRef] [PubMed] - Zee, M.; Davis, A.C.; Clark, A.D.; Wu, T.; Jones, S.P.; Waite, L.L.; Cummins, J.J.; Olson, N.A. Computational fluid dynamics modeling of cough transport in an aircraft cabin. Sci. Rep.
**2021**, 11, 23329. [Google Scholar] [CrossRef] [PubMed] - Ren, C.; Xi, C.; Wang, J.; Feng, Z.; Nasiri, F.; Cao, S.J.; Haghighat, F. Mitigating COVID-19 infection disease transmission in indoor environment using physical barriers. Sustain. Cities Soc.
**2021**, 74, 103175. [Google Scholar] [CrossRef] - Young, S.B. Evaluation of Pedestrian Walking Speeds in Airport Terminals. Transp. Res. Rec.
**1999**, 1674, 20–26. [Google Scholar] [CrossRef] - Rosti, M.E.; Olivieri, S.; Cavaiola, M.; Seminara, A.; Mazzino, A. Fluid dynamics of COVID-19 airborne infection suggests urgent data for a scientific design of social distancing. Sci. Rep.
**2020**, 10, 22426. [Google Scholar] [CrossRef] - Mittal, R.; Ni, R.; Seo, J.H. The flow physics of COVID-19. J. Fluid Mech.
**2020**, 894, F2. [Google Scholar] [CrossRef]

**Figure 1.**Visualisation of the developed agent-based simulation with agents, trajectories, and tracking of aerosols shown.

**Figure 2.**Interactions according to the underlying model of pedestrian dynamics between (

**a**) agents (shown as blue points) and obstacles (black rectangle) and (

**b**) between two agents, with associated quantities.

**Figure 3.**Exemplary visualisation of distance map ${\varphi}^{\mathrm{dist}}$ and directions ${\mathbf{G}}^{\mathrm{dir}}$, the associated destination point is located in the lower left in both cases. (

**a**) Colour-coded display of a distance map ${\varphi}^{\mathrm{dist}}$. (

**b**) Colour-coded display of directions ${\mathbf{G}}^{\mathrm{dir}}$, mapping of directions to colours is shown in the lower right.

**Figure 4.**Exemplary starting point configuration, individual starting positions are shown as blue points.

**Figure 5.**Detail view of trajectories and aerosol trail generation. (

**a**) Exemplary agent trajectories and aerosol trail generation. (

**b**) Detail view with agents, trajectories, and aerosol traces. (

**c**) Detail view showing only infectious agents and traces.

**Figure 8.**Simulations with one virus-variant of varying contagiousness: Number of infected agents over a simulated period of ten days. Shaded areas show respective minima and maxima.

**Figure 9.**Viral load thresholds ${c}_{0}^{\mathrm{crit}}=1.9\times {10}^{13}$ and ${c}_{1}^{\mathrm{crit}}=1.6\times {10}^{12}$. In this setting, only the numbers for the ratio 7:3 are significantly rising.

**Figure 10.**Viral load thresholds ${c}_{0}^{\mathrm{crit}}=1.9\times {10}^{13}$ and ${c}_{1}^{\mathrm{crit}}1.2\times {10}^{12}$. The number of infected is significantly rising for ratio 7:3, while for ratio 8:2 also rising, but much slower.

**Figure 11.**Viral load thresholds ${c}_{0}^{\mathrm{crit}}=1.9\times {10}^{13}$ and ${c}_{1}^{\mathrm{crit}}=0.8\times {10}^{12}$. Here, the numbers for ratio 7:3 are significantly rising with a jump after day 4. For ratio 8:2, the numbers are also significantly rising. Ratio 9:1 shows a rise towards the end of the ten-day-period.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Harweg, T.; Wagner, M.; Weichert, F.
Agent-Based Simulation for Infectious Disease Modelling over a Period of Multiple Days, with Application to an Airport Scenario. *Int. J. Environ. Res. Public Health* **2023**, *20*, 545.
https://doi.org/10.3390/ijerph20010545

**AMA Style**

Harweg T, Wagner M, Weichert F.
Agent-Based Simulation for Infectious Disease Modelling over a Period of Multiple Days, with Application to an Airport Scenario. *International Journal of Environmental Research and Public Health*. 2023; 20(1):545.
https://doi.org/10.3390/ijerph20010545

**Chicago/Turabian Style**

Harweg, Thomas, Mathias Wagner, and Frank Weichert.
2023. "Agent-Based Simulation for Infectious Disease Modelling over a Period of Multiple Days, with Application to an Airport Scenario" *International Journal of Environmental Research and Public Health* 20, no. 1: 545.
https://doi.org/10.3390/ijerph20010545