Prediction of local COVID-19 spread in Heidelberg

The transmission model and the parameters

We model the transmission dynamics of the COVID-19 outbreak by an individual level susceptible (S) – exposed (E) – infected (I) – removed (R; SEIR) compartmental model. The transitions between the compartments are described through the following set of differential equations

Where γ is the inverse of the infectious period and κ is the inverse of the incubation period. Extended data, Table 1⁶ lists all parameter choices for our model. For the main part of this manuscript we assume an incubation period of 5 days⁷ and an infectious period each of 2.9 days⁸. The infectiousness of the disease is given by R₀ and is defined as the mean number of people that get infected by a single infected individual over the whole infectious period. Due to the limited data about the COVID-19 pandemic, there is much uncertainty in the estimation of R₀. As baseline we follow the value of 2.2 obtained from the COVID-19 outbreak on the Diamond Princess ship⁹. For a sensitivity analysis, we also consider a lower R₀ of 1.5 with respect to the estimation of Du et al. (2020)¹⁰ and a more severe outbreak progression with 3 in accordance to the estimation of R₀ ranging between 2.2 and 3.6 for the SARS epidemic in 2003¹¹.

According to the office for statistics and urban development Heidelberg¹², for our model we assume a closed population of 150,000, without individual entering or leaving the system. We consider this as a realistic scenario because we do not expect major demographic changes to occur within the six months of the projections.

The true number of initial infected individuals remains unknown due to the asymptomatic progression in some cases. Furthermore, due to limited testing capacities, only high-risk individuals (i.e. people who had prior close contact to infected individuals or people returning from a high risk region according to the WHO definition) were tested, resulting in missing positive cases in the population that resulted from possible community transmission. To capture this uncertainty, we assume that the outbreak starts on 12 March 2020 with 10 initial infectious individuals who have not been isolated and are able to transmit the disease.

Countermeasures for reducing transmission

From these scenarios, it is obvious that lowering R₀ leads to a lowering of the final size of the epidemic, prolonging the peaking and minimizing the peak. The latter is the most important, as it avoids an outbreak trajectory, in which a large number of people get sick at the same time with overwhelming effects for the health system.

In the hope to lower the amount of secondary cases resulting from one primary case, on 22 March 2020, the German government announced the implementation of extraordinary measures to reduce social contact and thus transmission for at least two weeks. These include regulations on social distancing such as the closure of schools, kindergartens, shops, restaurants, imposing a visiting ban for hospitals and elderly homes, as well as preventing transmission amplification events and social interactions in public with more than two persons. Such countermeasures can be considered in the model by diminishing the transmission intensity R₀.

Figure 2 displays the progression of the outbreak in Heidelberg with respect to different reductions in social contact and thus disease transmission from Monday, March 23 onwards. It illustrates, that restricting social contact will have a major impact on the number of infected individuals per day, on the overall outbreak size and flatten the curve. In fact, a permanent transmission reduction by 30% will yield a total of 89,022 infected individuals by mid-September and 3,877 during the peak time (Figure 2a). Decreasing social contact by 50% will massively flatten the curve, with a total of 6,927 and 223 infected individuals at peak time. This will not stop the outbreak, but it will slow it down to a major extent. Considering the transmission on a scale of one year in time, with the permanent reduction of 50% of transmission, we will have 15% of the population of Heidelberg infected.

Figure 2. Possible outbreak progressions with reduction in social contact, thus disease transmission, after Monday, 23 March 2020.

The baseline transmission rate is R₀ = 2.2. (a) Permanent reduction of disease transmission over the next six months. (b) After three weeks of reduced transmission, transmission increases again by 50% of the reduction.

However, such a permanent lock-down of the population will not be feasible due to economical and psychological health reasons. Thus, in Figure 2b, we assume that after three weeks social life will be partially resumed and transmission rates will increase again by 50%. In this case, a transmission reduction by 70% at first with a following increase in contact rates (transmission reduction lowered to 35%) will lead to a total of 48,468 people infected by September. Compared to the worst-case scenario (permanent R₀ = 2.2) this is a decrease of 62% (78,106) in the total number of people infected.

If after three weeks contact rates will revert to their original state, the outbreak curve will only be shifted by weeks with no effect on the height nor on the outbreak size (see Extended data, Figure A3⁶).

Deaths, hospitalizations and ventilator capacity

As the severity of the disease and thus the number of expected deaths from the COVID-19 outbreak depends on the age of the individual, we obtained the specific age distribution for the city of Heidelberg: <55 (72.4%), 55–65 (11.06%), 65–75 (7.77%), and >75 years of age (8.77%)¹². Adapting from Dowd et al. (2020)¹⁴, the mortality probabilities for each age category are 0.1% (<55), 1.5% (55–65), 7% (65–75), and 20% (>75 years of age). By means of these percentages we calculated the cumulative number of deaths in Heidelberg as proportions of the people in the “Removed (R)” compartment over time (Figure 3) for different scenarios of transmission reduction. We model the delay between end of infectious period and time of death by 6.2 days and follow Sanche et al. (2020)¹⁵, who assume that the duration from hospital admittance to death is 11.2 days.

Figure 3. Expected number of cumulative deaths from COVID-19 in Heidelberg in the next six months.

As preparation for the health system to plan the bed and ventilator capacity that needs to be enabled, it is important to predict the number of patients who require hospitalization and ventilation.

It is difficult to give estimates for the proportion of hospitalization from all infected individuals, because there is an inherent bias in the existing data¹⁶. In the beginning of an epidemic, people are hospitalized for isolation purposes but not because of their severe symptoms. Besides, due to asymptomatic or minimally symptomatic infections that do not present for testing, the true number of infections remains unknown and thus estimates of hospitalization might be overly pessimistic. For this simulation study, we nevertheless assume, that 5% of all infected individuals need hospitalization. Because the duration of hospitalization varies in the literature, we take the smaller and more conservative estimate of 11.5 days^15,17,18 (Figure 4a). As the curves are proportions of the number of infected individuals, changing the proportion of hospitalizations will only change the scale of the plot. A sensitivity analysis reducing the duration of hospitalization to seven days is shown in Figure A3 in the appendix.

Figure 4. Number of hospitalized patients and number of ventilated patients per day.

For calculating the number of ventilators needed, we assume that 90% of all people who died from the disease were ventilated before. The remaining 10% possess a patient do not resuscitate/do not intubate (DNR/DNI) status. We further assume that 60% of ventilated die. This leads to 1.5 (0.9/0.6) people ventilated per death count. According to Chen et al. (2020)¹⁹, the average duration of ventilation is 3-20 days. Supposing a conservative estimate of 7 days, we can model the capacity in the Intensive Care Unit given the calculated death numbers.

According to the Science Media Center Germany, routine capacity for ventilation of the University Hospital Heidelberg is 112 spaces²⁰. Even if we unrealistically assume that all spaces can be used for COVID-19 patients, the capacity will not be enough within the following six months, unless we have a permanent reduction in the disease transmission by 50% (Figure 4b).

Underlying data

All data underlying the results are available as part of the article and no additional source data are required.

Extended data

Figshare: Prediction of local COVID-19 spread in Heidelberg - Supplementary Material. https://doi.org/10.6084/m9.figshare.12038664⁶.

This project contains the following extended data:

Extended are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0).