Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution.

License CC-BY-NC-ND. This is the accepted version of M. J. K¨uhn, D. Abele, T. Mitra, W. Koslow, M. Abedi, K. Rack, M. Siggel, S. Khailaie, M. Klitz, S. Binder, Luca Spataro, J. Gilg, J. Kleinert, M. H¨aberle, L. Pl¨otzke, C. D. Spinner, M. Stecher, X. X. Zhu, A. Basermann, M. Meyer-Hermann, ”Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution”. Mathematical Biosciences 339, 108648 (2021) published by Published by Elsevier Inc. The published journal article is available via https://www.sciencedirect.com/science/article/ pii/S0025556421000845.Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution Martin J. K¨uhna, Daniel Abelea, Tanmay Mitrab, Wadim Koslowa, Majid Abedib, Kathrin Racka, Martin Siggela, Sahamoddin Khailaieb, Margrit Klitza, Sebastian Binderb, Luca Spataroa, Jonas Gilga, Jan Kleinerta, Matthias H¨aberlec, Lena Pl¨otzkea, Christoph D. Spinnerd, Melanie Stechere, Xiao Xiang Zhuc, Michael Meyer-Hermannb,1, Achim Basermanna,1 aInstitute for Software Technology, Department of High-Performance Computing, German Aerospace Center, Cologne, Germany bDepartment of Systems Immunology and Braunschweig Integrated Centre of Systems Biology (BRICS), Helmholtz Centre for Infection Research, Braunschweig, Germany cEarth Observation Center, Department EO Data Science, German Aerospace Center, Weßling, Germany dTechnical University of Munich, School of Medicine, University Hospital rechts der Isar, Department of Internal Medicine II, Munich, Germany eUniversity Hospital of Cologne, Department I for Internal Medicine, University of Cologne; German Center for Infection Research (DZIF), Cologne, Germany Abstract Non-pharmaceutical interventions (NPIs) are important to mitigate the spread of infectious diseases as long as no vaccination or outstanding medical treatments are available. We assess the effectiveness of the sets of non-pharmaceutical interventions that were in place during the course of the Coronavirus disease 2019 (Covid-19) pandemic in Germany. Our results are based on hybrid models, combining SIR-type models on local scales with spatial resolution. In order to account for the age-dependence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we include realistic prepandemic and recently recorded contact patterns between age groups. The implementation of non-pharmaceutical interventions will occur on changed contact patterns, improved isolation, or reduced infectiousness when, e.g., wearing masks. In order to account for spatial heterogeneity, we use a graph approach and we include high-quality information on commuting activities combined with traveling information from social networks. The remaining uncertainty will be accounted for by a large number of randomized simulation runs. Based on the derived factors for the effectiveness of different non-pharmaceutical interventions over the past months, we provide different forecast scenarios for the upcoming time. Keywords: SARS-CoV-2, Covid-19, Coronavirus disease, Mitigation, Non-pharmaceutical interventions, Forecast 1. Introduction With more than 2.2 million reported deaths [1], the coronavirus disease 2019 (Covid-19) remains one of the most pressing issues for the whole globe. Already in October, WHO officials estimated that 10 % of the world’s population had been infected [2] and vaccination of the population will still take a considerable amount of time. Since exposing people is highly unethical [3], the only interim solution is to mitigate the spread of the disease by the application of non-pharmaceutical interventions. Email addresses: [email protected] (Martin J. K¨uhn), [email protected] (Michael Meyer-Hermann), [email protected] (Achim Basermann) 1Shared corresponding authors in alphabetic order. Preprint submitted to Mathematical Biosciences August 19, 2021 The assessment of non-pharmaceutical interventions and prediction by simulation has to be based on reliable models; cf. [4, 5, 6, 7, 8, 9, 10, 11] for the spread of SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) and other infectious diseases. Only then, the most effective interventions can be determined as a basis for informed political decisions. The aim of our study is to assess non-pharmaceutical interventions and to provide a reliable forecast of the Covid-19 pandemic in Germany based on four principles. First, we account for the age-dependence of SARS-CoV-2 [12, 13, 14]. Second, we include realistic contact patterns between different age groups [15, 16, 17, 18, 19]. Third, we include high-quality, spatially resolved information on commuting activities [20, 21] combined with traveling information based on the social network Twitter. Fourth, we combine all information and account for the remaining uncertainty by Monte-Carlo Ensemble runs. To our knowledge, such an in-depth study is not accounted for in the literature so far. The remainder of this paper is structured as follows. We first present our mathematical model and its numerical solution approach. Then, we present the social and non-pharmaceutical parameters used in our model and we discuss afterwards the epidemiological parameters obtained by extensive analyses. Our results are presented and discussed in the following. 2. Materials and methods 2.1. Model and solver There are various models to forecast the spread of infectious diseases across a country or community. Besides the well known SIR-type ODE models [22, 23], there are integro-differential models [22, 24], Bayesian Monte Carlo approaches [11], or agent-based models [25, 26]. While SIR-type models are praised for their simplicity and understandability, they lack for a good representation of spatial heterogeneity. To combine the advantages of a SIR model without loss of spatial resolution, we use multiple SIR-type models on a fine local scale and connect the compartments and age groups by graphs that represent traveling; cf. [27] among others. These SIR-type models can be easily exchanged by agent-based models due to the generic implementation of our graphs. This is integrated as part of our high performance modular epidemics simulation software MEMILIO that is continuously under development [28]. 2.1.1. Age-resolved SIR-type model The base of our SIR-type model can be found in the first version of [9]. Our model consists of the compartments Susceptible (S), healthy individuals without immune memory of SARS-CoV-2; Exposed (E), who carry the virus but are not yet infectious to others; Carrier (C), who carry the virus and are infectious to others but do not yet show symptoms (they may be preor asymptomatic); Infected (I), who carry the virus, are infectious and show symptoms; Hospitalized (H), who experience a severe development of the disease; In Intensive Care Unit (U); Dead (D); and Recovered (R), who cannot be infected again. To resolve age-specific disease parameters, we divide the totality of people Ninto ndifferent age groups. We then have Z:= Sn i=1 Zi:= Sn i=1{Si, Ei, Ci, Ii, Hi, Ui, Ri, Di}. For each age group i= 1, . . . , n, the transmission risk is denoted by ρiand the proportion of infected people not isolated or quarantined is denoted by ˜ βi; see Tables 1 and 2 for details. Infection results from contact with people from different age groups. We introduce the contact frequency matrix Φ = (φi,j)i,j=1,...,n,(1) where φi,j represents the (mean) daily contacts of a person of age group iwith people from age group j. We refer to [29] which states that ”the resulting matrix is not symmetric due to the different number of individuals in each age-group”. So due to the particularly chosen age groups and the demography of Germany, these contact matrices will be non-symmetric in our case. The naming convention for the remaining parameters can be understood as follows: We use the variables T∗2 ∗1for the time spent in state ∗1∈ Zibefore moving to state ∗2∈ Zi. For example, TRi Hi 2 Susceptible S Exposed E Carrier C Infected I Hospitalized H ICU U Recovered R Dead D φ ρ C+˜ βI N 1 TC E 1−µR C TI C µR C TR C 1−µH I TR I µH I TH I µU H TU H 1−µU H TR H µD U TD U 1−µD U TR U Figure 1: SIR-type model and strongest inter-county commuter activities. SIR-type model for one German county, based the on first version of [9] (left). We omit the age-dependence index ifor clarity; see Table 1 and 2 for a description of the parameters. Graph with center points of all German counties as nodes and edges according to commuter activity (right). Edges only shown where more than 10 000 workers commute on a daily basis. represents the time an individual in age group i= 1, . . . , n spent in the hospital before returning home due to recovery from the disease. Accordingly, µ∗2 ∗1represents the probability of a patient to transit to state ∗2when that patient is currently in state ∗1. The model, as expressed in Fig 1, is dSi dt =−Siρi n X j=1 φi,j Cj+˜ βjIj Nj ,(2) dEi dt =Siρi n X j=1 φi,j Cj+˜ βjIj Nj −1 TCi Ei Ei,(3) dCi dt =1 TCi Ei Ei− 1−µRi Ci TIi Ci +µRi Ci TRi Ci!Ci,(4) dIi dt =1−µRi Ci TIi Ci Ci− 1−µHi Ii TRi Ii +µHi Ii THi Ii!Ii,(5) dHi dt =µHi Ii THi Ii Ii− 1−µUi Hi TRi Hi +µUi Hi TUi Hi!Hi,(6) dUi dt =µUi Hi TUi Hi Hi− 1−µDi Ui TRi Ui +µDi Ui TDi Ui!Ui,(7) dRi dt =µRi Ci TRi Ci Ci+1−µHi Ii TRi Ii Ii+1−µUi Hi TRi Hi Hi+1−µDi Ui TRi Ui Ui,(8) dDi dt =µDi Ui TDi Ui Ui.(9) The equations (2)–(9) represent the transition of people from one state to another. Note that people in an age group Zicannot transit to another group Zjfor i6=j. In the section of the epidemiological parameters, we will discuss in detail which of the parameters we assume to be age-dependent and how this is included in our model. These findings are summarized in Tables 1 and 2. 3 Param. Description Reference Resources ρ(0) ρiage-dependent transmission risk Eq. (14),(2),(3) [30, 31, 32, 33, 34, 35, 36] kseasonality parameter Eq. (15), (14) [37, 38, 39, 40] ˜ βproportion of not isolated or quarantined symptomatic individuals Eq. (2), (3) Assumption. TC Eperiod of latent non-infectious stage Eq. (3), (4) [9, 41, 42] µR Cproportion of mild, asymptomatic cases Eq. (4), (5), (8) [43, 44, 45, 35, 46] TR Cperiod of asymptomatic stage before recovery Eq. (4), (8) [9] TI Cperiod of latent infectious stage Eq. (4), (5) [9, 41, 42] µH Iproportion of symptomatic cases needing hospitalization Eq. (5), (6), (8) [14, 47],[48, Report of Sept. 15] TH Iperiod of mild symptoms for individuals requiring hospitalization later on Eq. (5), (6), Suppl. Mat. [49, 50, 51] TR Iperiod of mild symptoms for individuals not requiring hospitalization later on Eq. (5), (8) [52, 9] µU Hproportion of hospitalized individuals getting ICU treatment Eq. (6), (7), (8) [53, 54, 47] TU Hperiod of hospitalization before ICU treatment (of critical cases) Eq. (6), (7), Suppl. Mat. [49, 50] TR Hperiod of hospitalization before recovery (of non-critical cases) Eq. (6), (8), Suppl. Mat [9] µD Uproportion of individuals in ICU care that die Eq. (7), (8), (9), Fig 4 [54, 55] TR Uperiod of ICU treatment before recovery Eq. (7), (8), Suppl. Mat [9, 56, 50] TD Uperiod of ICU treatment before death Eq. (7), (9), Suppl. Mat [50, 9] Table 1: Description of parameters and main resources for their derivation. 2.1.2. Spatial resolution While SIR-type models are straightforward to apply and interpret, they lack the possibility of modeling local effects or spatial heterogeneity. In order to avoid averaging over important effects such as infection clusters, we assign one particular age-resolved model to each county. We represent each county by a node of a (directed) graph. The edges of the graph represent the connections between the different counties and are weighted with the number of people commuting daily and traveling on average. The edges do not only hold single values (weights) for how many people daily commute between different counties but also coefficients to determine the proportion of people of different age groups and compartments that commute or travel. Doing so, we can restrict travel activities to healthy or only mildly infected individuals. Let nCbe the number of counties (nodes of the graph). Then, for two nodes akand al, 1≤k, l ≤nC, the weight wk,l on edge ek,l represents the proportion of people going daily from ak to al. 2.1.3. Numerical solver Common numerical solvers for the system of nonlinear ordinary differential equations (2)-(9) are semi-implicit or adaptive explicit. While the former allow for larger time steps, the latter allow adaptive time steps to prevent large numerical errors. We have implemented an adaptive RungeKutta-Fehlberg45 (RKF45) method [57] that uses methods of 4th and 5th order and solves the equations without excessively small time steps. The numerical procedure becomes more challenging when we also resolve the equations spatially. For this, we define a commuter as a person who travels from county akto al, 1 ≤k, l ≤nCand back again within one day (whether it is work or free time related). Given start values from day t, we 4 range in age group param. 0-4 5-14 15-34 35-59 60-79 80+ ρ(0) [0.02,0.04] [0.05,0.07] [0.08,0.10] [0.15,0.20] k[0.1,0.3] ˜ βsigmoidal curve from [0.1,0.3] to [0.3,0.5] TC E[2.67,4.00] µR C[0.20,0.30] [0.15,0.25] TR CTI C+ 0.5TR I TI Csampled with TC Eand (16), incubation period = 5.2 µH I[0.006,0.009] [0.015,0.023] [0.049,0.074] [0.15,0.18] [0.20,0.25] TH I[9,12] [5,7] TR I[5.6,8.4] µU H[0.05,0.10] [0.10,0.20] [0.25,0.35] [0.35,0.45] TU H[3,7] TR H[4,6] [5,7] [7,9] [9,11] [13,17] µD U[0.00,0.10] [0.10,0.18] [0.3,0.5] [0.5,0.7] TR U[5,9] [14,21] [10,15] TD U[4,8] [15,18] [10,12] Table 2: Summary of the age-dependency of parameters and their ranges. advance our adaptive RKF45 solver for 0.5 days. Next, we allow people to commute or travel. Their amount is defined by the commuter rate between two counties, namely the weights wk,l introduced in the previous section and further specified in following section. Note that commuting also depends on the infection state since hospitalized individuals cannot commute and infected individuals will travel less than healthy ones. For the latter, we assume the same level of isolation or quarantine as on county level. With the updated population, we again advance our adaptive solver for 0.5 days. Additionally, we conduct an auxiliary step with step size of 0.5 days with an explicit Euler solver where we only consider the in-commuters, using the county’s population as contact population only. This step is executed since, after the high precision scheme from t+ 0.5 to t+ 1, we do not know the updated state of our commuters (e.g., susceptible may have become exposed or carriers have become symptomatic). This is due to the nature of the SIR model (2)-(9) that does not keep track of individuals. Still, the commuters have to go back to their home county, and we need to know their most likely infection state. We use the results from the explicit Euler step, to quantify the proportion of individuals of the different compartments that return. With this estimation, we start the returning process. These considerations are summarized in Fig 2. 2.2. Social and non-pharmaceutical parameters The spread of SARS-CoV-2 depends on many parameters. While some of these parameters are inherent to the virus, others depend on social contact patterns and non-pharmaceutical interventions introduced by decision makers. In this section, we will focus on non-pharmaceutical interventions and their influence on contact patterns and commuter rates in our model. 2.2.1. Inter-county travel Let us first continue with the spatial resolution of our model and focus on how we specify the rate of work or leisure commuters wk,l between different counties akand al. To estimate wk,l on 5 Figure 3: Inter-age group contact patterns. Combined prepandemic contact patterns φGer Bof [17, 16] for Germany interpolated to age intervals as provided by [62] (top). Extrapolated, pandemic contact patterns φGer Mfor simulated lockdown phase for Germany (as of end March in the UK; based on contact study [18]) (bottom). bigger cities like Hamburg, Hannover, Cologne, or Stuttgart. Assuming that the mobility obtained from Twitter accounts for 20 % of all travel activities (work commuting, student commuting, leisure travel etc.), we scale the twitter matrix accordingly. The resulting values are divided by the population size and the result will be denoted by tk,l, 1≤k, l ≤nC. The amount of mobility in our model is given be the edge weights ek,l of the graph. These weights are derived from the matrix ck,l for the work commuters and from tk,l for the ‘Twitter’ activities. The weights also depend on the implementation of non-pharmaceutical interventions. In particular, they depend on the NPI related parameters r(∗) W,i,i for work and r(∗) O,i,i for ”other” places related measures that mainly affect free-time activities. Here, ∗ ∈ {1,2}and i= 1, . . . , n are the corresponding age groups; see the corresponding section and Table 3 for details on these parameters. The commuter matrices contain many insignificant coefficients close to zero. These are due to loosely coupled regions where only a very limited number of individuals commute on a daily basis (e.g., 1 or 2). To reduce the computational effort, we eliminate edges ek,l where ck,l <4·10−5and tk,l <1·10−5. The cutoff values are chosen so only 1 % of information is dropped and that more than 99 % of travels are included. We also paid attention to reflect the above assumption that Twitter data represents 20 % of travels. With this procedure, the number of edges is reduced by approximately 60 % and the computational efficiency is increased significantly. 2.2.2. Contact patterns in Germany In the following, we focus on the intra-county contact patterns. In this section, we derive a baseline, prepandemic contact matrix φGer Band a minimum contact matrix φGer Mfor a simulated strict lockdown in Germany. As SARS-CoV-2 transmission occurs mainly during human-to-human interaction, reducing contacts can efficiently slow down the spread of the disease; cf. [63, 15, 16, 17] for literature on contacts and the spread of infectious diseases. However, lockdowns which effectively reduce contacts to a minimum should be avoided due to their profound negative impact on many individuals and communities [3]. Therefore, the challenge for today’s decision makers is to find the most appropriate and effective interventions for the actual developments. Prepandemic patterns. In order to quantify the potential of transmission reduction by contact 7 pattern changes, good prepandemic as well as recent data is needed. From [15] and its projections [17], we use realistic contact patterns for Germany split up into the categories “Home”, “School”, “Work”, and “Other”. In [15], contacts are defined as skin-to-skin contact, or where at least three words were exchanged. For the particular case of school contacts, the mean numbers of contacts recorded in [15] are rather low for Germany. Given the fact of aerosol transmission risk in closed spaces, we suggest to assume slightly higher contact rates for a conservative estimate on the spread of the disease. Further information is offered by the demography-based school contact matrix in [16]. We use the quotient of the maximum eigenvalues between both matrices to scale the contact matrix of [17] which then results in a larger number of school contacts. The combination of baseline contacts for “Home”, “Work”, and “Other” from [15, 17] and for “School” based on the comparison of [17, 16] results in the contact matrix φGer B; cf. Fig 3 (top). SARS-CoV-2-related minimum patterns. The potential of possible contact reduction is limited by the minimum number of necessary contacts that keep essential sectors of the society running. To assess this, we consider the contact study [18], that started during the lockdown phase in the United Kingdom. By the end of March, many ‘non-essential’ parts of the economy were shut down and social interaction was limited to a minimum [64]. This study yields the minimum contact matrix ΦUK M. The matrix ΦUK Mis missing values since only individuals aged 18 or older participated in [18]. In order to fill out the missing information, we follow a strategy similar to [65]. We employ the prepandemic/baseline contact matrix ΦUK Bfrom [17]. We scale this matrix by the ratio of the dominant eigenvalues λBand λMof the lower-right, square matrices (φUK ∗,i,j,)i,j≥3,∗ ∈ {M, B}. Then, we use this scaled version to fill out the missing subset φUK M,i,j =φUK B,i,j ·λM λB ∀i∈ {1,2}, j ∈ {1, ..., 6}.(10) We aim at deriving a minimum contact matrix φGer Mfor a simulated strictest lockdown in Germany. We consider the number of contacts in the UK by the end of March to be a minimum that we can achieve in a SARS-CoV-2-related lockdown. From the UK data, we consider the quotient of contact reduction di,j =φUK B,i,j /φUK M,i,j ∀i, j ∈ {1,...,6},(11) and apply these factors to the matrices φGer B,i,j derived from [17, 16] φGer M,i,j =di,j ∗φGer B,i,j ∀i, j ∈ {1,...,6}.(12) In Fig 3, the minimum ΦGer Mis shown at the bottom. Note that the single entries given in the bottom row of Fig 3 are not required to be smaller than the ones in the top row. The minimum of contacts during lockdown is to be understood as the minimum of total contacts of all individuals. Locally, for one location and the interaction of two age groups, the mean contacts could even increase slightly. The difference between the top and bottom of Fig 3 defines realistic boundaries for all non-pharmaceutical interventions that could possibly be implemented. To assess uncertainty, we allow for a 5-10 % deviance of the given values in our ensemble runs. From [66], we have an estimated contact reduction during spring lockdown in Germany of 63 %, taking the minimum values here, we could achieve a contact reduction of 76 %. 2.2.3. Contact-related interventions There are two ways to reduce potentially dangerous contacts, namely, to avoid the contacts (first level of reduction) at all or to wear masks, keep distance and ventilate closed spaces (second level). While the mean number of daily contacts in Germany is lower than in many other European countries, a relatively large percentage of contacts happens at workplaces [15]. Hence, many transmissions can be avoided by working from home whenever possible. From a recent analysis of 8 intervention implementation factor ranges comment working weak r(1) W,i,j ∈[0.0,0.1] from intermediate r(1) W,i,j ∈[0.2,0.3] home strong r(1) W,i,j ∈[0.4,0.5] partial school none r(1) S,i,j = 0.0 closures and weak r(1) S,i,j = 0.25 remote intermediate r(1) S,i,j = 0.5 schooling complete r(1) S,i,j = 1 gathering bans, weak r(1) O,i,j ∈[0.0,0.2] additional increase of (partial) closing rather weak r(1) O,i,j ∈[0.2,0.4] r(1) W,i,j by 0.05 to 0.20, of bars, intermediate r(1) O,i,j ∈[0.4,0.6] according to strictness; restaurants, strong r(1) O,i,j ∈[0.6,0.8] cf. corresp. section cinemas etc. very strong r(1) O,i,j ∈[0.8,1.0] face masks, weak r(2) ∗,i,j ∈[0.0,0.2] distancing, rather weak r(2) ∗,i,j ∈[0.2,0.4] regular intermediate r(2) ∗,i,j ∈[0.4,0.6] ∗ ∈ {H, S, W, O} ventilation of strong r(2) ∗,i,j ∈[0.6,0.8] closed spaces very strong r(2) ∗,i,j ∈[0.8,1.0] Table 3: Summary of different non-pharmaceutical interventions and implementations in simulations. Germany [21], up to 40-50 % of the population could work from home if necessary. We suppose that in the prepandemic phase “home office” was only used by 5 % with as much as 20-35 % working from home during different phases of the pandemic [21, pp. 96-101]. Further contact reduction is induced by people who stop working altogether, so these values have to be subtracted from the prepandemic matrix. We know that about 20 % of the population stopped working in March and April [21, p. 96]. For the less strict interventions, we assume values of 5-10 %. While working from home is feasible for a larger part of the population, global school closures and the resulting home schooling “present an unprecedented risk to children’s education, protection and well-being” [67]. Apart from school closures, contacts in schools can be reduced by smaller classes where possible, fixed seating arrangements, regular ventilation, or pooled testing [68]. There are a number of further locations where contact reductions are feasible such as bars, restaurants, supermarkets, or public transport. We here include the effect of interventions such as face masks, distancing etc. In many studies such as [38, 69], face coverings and ejected air flows while breathing, speaking, or coughing are studied. The meta analyses in [70] and [71] find (large) protective effects of face masks for SARSCoV-2 transmission such as 40 % or even a pooled odds ratio of 0.35. In particular, the protective effect of community-wide masks is shown in [72]. We will consider different risk reduction ranges for wearing masks combined with keeping distance and regular ventilation of closed spaces. In the predictive analysis of the spread of infectious diseases, not only non-pharmaceutical interventions and one-time contact changes but also adherence to interventions is important. While there is a small decrease in adherence to preventive measures observed in [19, 73] after months of the pandemic, the adherence is still large and rather stable with an even increasing number of people wearing masks [73] (e.g., 93 % wear them often or always). In the consequence, we do not include these opposing effects in our simulations. In the results section, we vary the strictness of the interventions according to the political decisions and Table 3. 9 ∗ ∈ {H, S, W, O}, which is a quite strong measure for distancing, face masks and other interventions. Simulation. Our initial conditions are derived from the age-resolved case data provided by [62]. We take confirmed cases around the start date of our simulation from which we extrapolate the compartments in eq. (2)-(9) by using the parameters in Table 2. Based on [84] and our parameters, we extrapolate age-resolved ICU data. In order to obtain age-resolved ICU data, we slightly reduce the initial extrapolation of 80+ intensive care cases since too large death rates occur in the beginning part of the simulation otherwise. We refrain from further correction of initial values without having more reliable data. Given positive rates of 1 % or less during summer [48, Report of Aug. 26], we assume that the number of unknown symptomatic infections was small. Therefore, we start our simulations on June 1, July 15, and September 1 directly from the number of confirmed cases. Given the increased proportion of positive tests up to mid of October, we start the the simulations with a twofold of the confirmed cases. For each scenario, we run 1000 Monte Carlo runs such that we have a reliable set of parameters sampled in the given ranges. For the runs, we provide the median values as well as the percentiles obtained from the simulation runs. We use a seven day moving average of real world data and extrapolate the day of death, using the parameters from Table 2. 2.4.3. Discussion of Retrospective Scenarios In the following, we discuss the results of the four different retrospective scenarios with the described sets of implemented NPIs over time. We compare the overall and the age-resolved death rates with the extrapolated real data. We also compare the overall infection rates and the ICU occupancy. In the corresponding Figures 5, 7, 9, and 11, we present the median (percentile p50) and the percentiles ranges from (p05 and p95) as well as p25 and p75 as explained above. Additionally, in the maps of Figures 6, 8, 10, and 12, we show two snapshots of the regional spread of the infection, where we compare the extrapolated real data on the left with our simulation on the right. Note that the scaling of the color bars differs for the scenarios and represents the relative number of infections per 100 000 inhabitants. Scenario 1. Our first scenario (S1) is computed 45 days from June 1 onward. During the summer months, we observe only a slow rise in the infections in the RKI data and a decrease of ICU occupancy from DIVI (Fig 5). Both are captured well with the median of our simulations. The small elevation in the number of infections in June is due to an outbreak of Covid-19 in a slaughterhouse in G¨utersloh. As expected, we cannot capture such a stochastic event. Focusing on the first part of June (see Figure 6, top), we observe further regions that are underestimated by our simulation and some where it is the other way around. Overall, however, a larger incidence in the RKI data mostly corresponds to a larger incidence in the simulation data. Note that overand underestimating also happens due to a different strictness of local interventions. Worth mentioning is the spread of infections into neighbouring regions which we can see for Berlin from the middle to the bottom. Due to the inclusion of mobility, we see that the infection spreads into the near regions in our simulation (right) as in the extrapolated real data (left). Due to the longer simulation time, the results on the bottom show further deviation from the data. In Figure 5, we plot the median death rate, the percentiles and the extrapolated real data for the different age groups. Our model is quite close to the overall death rate. The age group 60-79 years is captured very well and the age groups below are also captured well. We are a little less close for the age group 80+ years. The deviations are to be expected since we aim for an overall good fit of our model without tweaking it for the individual scenarios. Additionally, we lack age-resolved ICU occupancy data and have to extrapolate the intensive care input data for the different age groups. This then also affects the simulated death rates. Note that the age groups below 15 years only contribute marginally to the death rate. The deviance with simulation seems large, but due to the small numbers (0 or 1), we are actually close to the real world value. Scenario 2. Our second scenario (S2) is computed 45 days from July 15 onward. The results of this Scenario are very similar to the results of S1. This holds for the overall death rates and the death rates in the different age groups as depicted in Figure 7. A main difference is the influence of travel returners [48, Report of Aug. 9] that might be responsible for the rise of infected in the 16 and Research for the project CoViDec (FKZ: 01KI20102). The funding bodies had no role in the design of the study, collection, analysis, and interpretation of the results, or writing the manuscript. Conflict of interest. Dr. Spinner reports no conflict of interest during the conduct of the study; but personal fees from AbbVie, grants and personal fees from Aperion, grants and personal fees from JanssenCilag, grants and personal fees from Gilead Sciences, personal fees from molecular partners, grants and personal fees from MSD, grants and personal fees from ViiV Healthcare/GSK, outside the submitted work. All other authors declare that they have no conflict of interest. Acknowledgements. We thank Valerie Grappendorf, a student at the Hochschule f¨ur Gestaltung Schw¨abisch Gm¨und, for contributing Fig 2. We express our deep gratitude to all study teams supporting the LEOSS study. The LEOSS study group contributed at least 5 per mille to the analyses of this study: C. Spinner, S. Rieg, F. Hanses, S. Borgmann, M. Hower, M. Vehreschild, M. M. R¨uthrich, L. Tometten, C. Piepel, S. Dolff, K. Wille, J. Lanzster, M. von Bergwelt-Baildon, U. Merle, C. R¨ommele, C. Degenhardt, J. F¨urst, S. Dalin, N. 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