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Article

Coronavirus modelling at the NIPH

Published Updated

This page briefly describes the model used by the NIPH for situational awareness and forecasting of the coronavirus outbreak in Norway. The reproduction number (R) can be found in the daily reports listed below.

coronavirusmodellering.JPG

This page briefly describes the model used by the NIPH for situational awareness and forecasting of the coronavirus outbreak in Norway. The reproduction number (R) can be found in the daily reports listed below.


Newest national report

A list of earlier reports from the modelling group can be found at the end of this page. In each report you will find R in table 1.

26th August 2020

R5 represents the reproduction number from August 1. As there is a delay of about 2 weeks from the time of infection to a hospitalisation, the model has no information about the number of infections today, but about the first part of August.

We change the model regularly and set new reproduction numbers so that the latest reproduction number are as up-to-date as possible about the latest developments.

The model needs data to estimate R5, and, when there is little data, the uncertainty will be great. Therefore, we wait about 3 weeks, before we switch to a reproduction number that will say something about the development in August.

29th June 2020

In the report published on the 29th June 2020, a new reproduction number (Reff3) was introduced for the period from 11th May 2020, with a new method, Sequential Monte Carlo, to estimated daily R values.

16th May 2020 

In the report published on 16th May 2020, the following were new:

  • The meta-population model is calibrated to the number of new patients admitted to hospital (incidence data). Previously, the model was calibrated to the total new admissions (prevalence data). 
  • Time spent in hospital and time spent on a respirator are estimated using Norwegian data. Previously, data from international reports were used.

4th May 2020

In the report publishedon the 4th May 2020, a new reproduction number (Reff2) was introduced for the period from 20th April to 3rd May 2020. See the sections about Calibration and Uncertainty below.

 

Reproduction number (R)

Updates to the reproduction number are also published in the weekly reports.

The model estimates of the reproduction number depend greatly on trends in the number of patients admitted to hospital with a COVID-19 diagnosis in Norway. Since the infection burden in Norway is at a stable, low level, and the number of patients who are admitted to hospital is low and declining, frequent model estimates of R do not give valuable additional information. Therefore, the NIPH has chosen to publish the updated R number in the weekly reports.

Uncertainty

There is still considerable uncertainty associated with the course of COVID-19 disease and about how many people require hospitalisation and treatment. This has consequences for the model predictions.

We handle this uncertainty to some extent with stochastic (random) simulations. We continuously update the parameters in the model as new knowledge and better data become available. We are constantly working to improve the methods we use to estimate the model parameters from the data.

Meta-population model

The model is a stochastic SEIR-type model with a local transmission process in each municipality. The spread between municipalities is modelled by following how people travel between municipalities. The amount of travel between the different municipalities is based on mobile phone data from Telenor. The model is a further development of Engebretsen et al. (2019) and Engebretsen et al. (2020).

Several articles (Ferretti et al 2020, ECDC report, LSHTM report) have pointed to the importance of pre-symptomatic infection so we include pre-symptomatic and asymptomatic infection in the model. A schematic overview of the epidemiological model is illustrated below:

The latest reports, with further details of the model, can be found in the list below.

coronavirusmodellering.JPG
A schematic overview of the epidemiological model.

Mobility data from Telenor Norway show how many people have travelled from municipality A to municipality B during each 6-hour intervals every day. We simulate mobility by moving people every 6 hours, according to the mobility data. Between the transfers, we allow everyone to mix for 6 hours, so that the virus can transmit among people in each municipality by contact between infectious individuals and susceptible individuals.

The model implementation is available on GitHub. We use the asymmetric_mobility_se1e2iiar model from this package.

The model gives us time series for the number of individuals in each disease state (the classes in the figure above) in each municipality. We use predicted incidence in each municipality to simulate the number of hospitalisations, intensive care patients and deaths.

Model parameters

For the transmission part of the model, we use data from Ferretti et al. (2020), with some minor changes based on the ECDC report on the pre-symptomatic period.

Parameters

Value

Exposed period

3 days

Pre-symptomatic period

2 days

Symptomatic infectious period

5 days

Infectiousness pre-symptomatic

1.25

Proportion asymptomatic

40 %

Infectiousness asymptomatic

0.1

For the proportion who need hospitalisation, we use age-based rates based on data from Verity et al. (2020) adjusted for the proportion in nursing homes and scaled by 1/3 so that the death rate in Norway is 0.3 per cent per infection, which is more in line with recent international data (Global Covid-19 Case Fatality Rates, CEBM.

 

Parameter

Value

Time spent in hospital

See figure 2 below

Risk of hospitalisation (total)

3.9 %

Hospitalisations per infection

0- 9 years

10-19 years

20- 29 years

30-39 years

40-49 years

50-59 years

60-69 years

70-79 years

80+ years

 

0,2 % (Salje et al, 2020)

0,2 %

0,6 %

1,3 %

1,7 %

3,5 %

7,1 %

11,3 %*

27 %*

Symptom onset to hospitalisation

9 days (neg. biomial)

Percentage in Intensive care unit:

februar-mars

20 %

april

10 %

mai

15,1 %

* The proportion of hospital admissions is reduced since nursing home residents are not usually admitted.

skisse over pasientflyt i modellen
Figur 2. Modellering. . FHI.

Calibration

One of the key parameters in the model is the reproduction number. We calibrate the model and estimate the reproduction number so that the model is adapted to hospital admissions on a national level. Since the test criteria have changed during the epidemic, hospital admissions provide a more robust way of characterising developments, although we have a delay effect because infected individuals might need hospitalisation only later in the course of their diseases.

We begin the calibration by taking into account all confirmed imported cases from abroad before 19th March. We place them in their residential communities on the date they developed symptoms, in the symptomatic class. Since there are likely to be more imported cases than those confirmed, we include an amplification factor that we also calibrate on data on hospital admissions.

We vary the estimated reproduction number along the way in the model, and define R0 (the reproduction number at the beginning of the model) and Reff1 and Reff2 acting after the start of implemented measures.

  • R0 is used from 17th February to 14th March
  • Reff1 from 15th March to 19th April 
  • Reff2 from 20th April to 10th May
  • Reff3 from 11th May

The 15th March was chosen because it provides the best fit for hospital admissions.

We calibrate these together with the amplification factor by on a logarithmic scale. As the guidelines and measures change, we will make several changes to the reproduction rate when necessary.

Uncertainty

The results from the model are subject to uncertainty due to randomness in spread and mobility (whether infectious or susceptible people travel, for example) and uncertainty in the estimated parameters. In addition, there are several sources of uncertainty that the model does not capture, as we do not take into account uncertainty associated with the model's other parameters. The model is a simplified representation of reality and is based on an assumption of average behaviour in the population across ages.

The number of patients admitted to hospital is based on the parameters that quantify the proportion of infected patients admitted to hospital. This has major uncertainties and impacts significantly estimates of the number of people who have been infected in Norway. As new knowledge suggests that fewer of those infected need to be admitted to hospital, and as the model is based on the number of hospital admissions in Norway, the estimate for the number of infected in Norway has been adjusted upwards in the model from week 16.

Soon we hope to update more parameters in the model about healthcare sector use to Norwegian conditions using data from the Preparedness register. For better predictions, it will be essential to obtain data from planned prevalence studies. These data can significantly change the estimated proportions in hospital.

The model does not contain an age structure, and transmission between different age groups is therefore not captured. Advice that the elderly should not have contact with others and thus reduce their risk of infection is, for example, not included in the model.

Interpretation of results

The results of the model should be interpreted with caution and must always be viewed in the context of other information and with epidemiological assessments. As mentioned above, there are many moments of uncertainty and the model is constantly improved.

In the model, hospital data are used to understand the evolution of the epidemic. If estimates of admissions do not match the model's estimates, it means that the model must be revised to better describe the developments we are observing. If other data are not well described by the model, it probably means that some of the parameters do not describe the situation in Norway well enough. We try to update these parameters as soon as we get updated information.

Modifications to the model

The model is dynamic and we update it when we receive new information from Norway or abroad. Major changes are described in the detailed report.

Other COVID-19 models developed by NIPH

In addition to the metapopulation model we have described above, the NIPH is developing an individual-based COVID-19 model based on a published model in Di Ruscio et al. (2019) that was developed to study the spread of methicillin-resistant S. aureus in Norway. In this model, the spread of infection is simulated in detail and the model can be used to estimate the effect of measures such as closing schools or working from home. This model can also look at effects among different age groups. We have also developed a national age structure model to assess the effects of possible vaccines against COVID-19. In this national model, we use data from the Directorate of Health on risk groups for COVID-19 and the number of healthcare professionals working actively in the healthcare sector for targeted vaccination.

Lokale rapporter

Nasjonale rapporter

Rapporter april-juni 2020

History

12.06.2020
Added section about Other COVID-19 models developed by NIPH

22.5.2020: tables updated, figure 2 published.

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