Agent-based modeling to estimate the impact of lockdown scenarios and events on a pandemic exemplified on SARS-CoV-2

Abstract

In actual pandemic situations like COVID-19, it is important to understand the influence of single mitigation measures as well as combinations to create most dynamic impact for lockdown scenarios. Therefore we created an agent-based model (ABM) to simulate the spread of SARS-CoV-2 in an abstract city model with several types of places and agents. In comparison to infection numbers in Germany our ABM could be shown to behave similarly during the first wave. In our model, we implemented the possibility to test the effectiveness of mitigation measures and lockdown scenarios on the course of the pandemic. In this context, we focused on parameters of local events as possible mitigation measures and ran simulations, including varying size, duration, frequency and the proportion of events. The majority of changes to single event parameters, with the exception of frequency, showed only a small influence on the overall course of the pandemic. By applying different lockdown scenarios in our simulations, we could observe drastic changes in the number of infections per day. Depending on the lockdown strategy, we even observed a delayed peak in infection numbers of the second wave. As an advantage of the developed ABM, it is possible to analyze the individual risk of single agents during the pandemic. In contrast to standard or adjusted ODEs, we observed a 21% (with masks) / 48% (without masks) increased risk for single reappearing participants on local events, with a linearly increasing risk based on the length of the events.

Keywords: Agent-based modeling; COVID-19; Individual transfection risk; Lockdown scenarios; Mitigation measure simulation; SARS-CoV-2.

Figure 1

Flowchart for the possible states of an agent. Only agents in one of the states $\{I_0,I_1,I_2,H\}$ are able to infect susceptible agents (state S) if they have contact with each other.

Figure 2

The extinction probability (heat color coded 0% to 100%) is given for the combination of multi-spreader (row) and normal spreader (column) at the begin of the simulation. Probabilities were estimated based on 100 simulation runs per parameter setting.

Figure 3

Fitted ordinary differential equation model (Susceptible-Exposed-Infected-Recovered) to observed data from the ABM. ABM states were transformed into SEIR states according to Eq. (2). Light dashed lines are representing the ODE states of SEIR and the corresponding dark solid lines represent the transformed ABM states (light red, red: S; light purple, purple: E; light green, green: I; light blue, blue: R).

Figure 4

(A) Development of infection numbers in relation to the peak of the first wave. For all urban districts the date of the peak for whole Germany were chosen. (B) Simulation runs for different random seeds. The social distancing parameter $\kappa$ was used to fit the simulation data to observed infections in Germany.

Figure 5

Infections per day for all mitigation scenarios for 49 days lockdown (A) and lockdown until the end of the simulation (B). Grey shaded regions mean, that a lockdown scenario is active.

Figure 6

(A–D) Box-Whisker-Plots represent distribution of amount of days until 5% of agents got infected within 10 simulation runs with different random seeds. (A) size of the event, (B) time of the event, (C) percentage of reappearing attendees, (D) frequency of events per week. Coloring of boxplots show the different lockdown scenarios (dark green: events without mask, light green: events with masks, grey: no events).

Figure 7

Investigation of infection curves for the event frequency as the parameter with the strongest influence. Lowest ((A) and (C)) vs Highest ((B) and (D)) event frequency is shown for the whole simulation run. Lines are showing the mean infection numbers of the 10 simulation runs for each setting. Shaded regions are showing the min/max region for the 10 runs. In (C) and (D) only the lockdown period is shown.

Figure 8

Proportion of infections caused on events compared to infections occuring at the same time offside of events for (A) events allowed during lockdown with masks and (C) events allowed during lockdown even without masks. Infections per hour were compared by measuring infections per 100,000 agents in (B) and (D).

Figure 9

Proportion of susceptibles for non-event participants, event participants with masks and event participants without masks for the whole time period (A) and for the lockdown period (B).

Figure 10

Increase of individual risk for reappearing attendees (wearing masks) compared to non-event participants during the lockdown. Size and Duration were varied, all other parameters were kept as in our standard event setting.