Modelling the outcome of Dutch government coronavirus response

TODO:

• Split the model up into different age groups with different mu
  • Plot deaths per age group

Data sources

RIVM data

Overview of all data: link

• Number of contagious people (prevalence): link
• Number of positively tested people in the Netherlands, updated each day at 10:00 CEST: link
• Each case of positive test, with first day of illness, age etc: link
• Reproductive number: link
• More raw data: link
• Behaviour studies: link
• COVID-19 new cases, hospital admission and death rates per municipality: link
• Data on all tests performed (total number, number positive): link

Weekly update link with:

• Number of tests performed per week
• Infection context, like at home, at work, pub etc.

Other Dutch data

A huge list of data sources: link

Predictions: link

NICE intensive care data: link

Corona Locator, with a plethora of data: link

• Up to date clusters: link

Weather data: KNMI

Other international data

Superspreader event database: article, Google docs database

SARS-COV-2 strains: link

Possible early predictors (for prevalence and R)

Mobility data:

• Apple
• Google

Sewage measurements:

• data
• info

Government response

Overview

Raw data

Codebook that indicates the meaning for various flags etc. Methodology for calculating the indices.

Single country single day API

Timeline of coronavirus in the Netherlands, including each change in government response: link

Detailed statistics

Incubation period

• 8.3 days (median is 7.76 days), looks kind of exponential (or Poisson) link
• 5.1 days: link
• 4-5 days: link
• 5.08 days (46% asymptomatic infections): link
• 6.93 days in India link

Case mortality rate (IFR):

• 1.4% for the Netherlands: link
• 0.68% average worldwide: link

Days contagious after infection link

• Up to the 11 day

IC rates information

• 13.8% of infections are severe, 6.1% are critical link
• Hospitalization based on age: link

Data visualization

covid-analytics.nl: the general test positivity rate graphs etc, but also detailed and complete information on hospital bed/ICU usage and up to date capacity.

CoronaWatchNL

Analysis

Impact of humidity

Predicting the reproductive number R with the following input parameters since 15-6-2020 (starting date at which R measurements became more reliable):

'retail_recreation_smooth',
'transit_stations_smooth',
'residential_smooth',
'workplaces_smooth',
'driving_smooth',
'walking_smooth',
'transit_smooth',
'Rad',
'TAvg'

Gives a 20% test set R^2 = 0.851. Now to tinker with the data (date of tinkering: 16-12-2020):

• Removing TAvg (average daily temperature) gives a test set R^2 = 0.841.
• Removing TAvg and adding HumAvg (average daily relative humidity) gives a test set R^2 = 0.842.
• Adding HumAvg (and having TAvg included too) gives a test set R^2 = 0.854.
• Removing TAvg and adding HumAbsAvg (average daily absolute humidity) gives a test set R^2 = 0.854.
• Adding HumAbsAvg (and having TAvg included too) gives a test set R^2 = 0.854.

So adding the HumAvg parameter "adds" an R^2 of ~0.003, barely any impact. The HumAbsAvg parameter has the same impact as the temperature. The temperature is part of the calculation for the absolute humidity from the relative humidity, so it seems that the temperature is the sole impact factor.

When looking at the correlation matrix we obtain the following Pearson correlation coefficients for the weather parameters:

• Average daily solar radiation [J/cm^2]: 0.161
• Average daily temperature [C]: -0.026
• Average daily relative humidity [%]: 0.065
• Average daily absolute humidity [g/kg]: 0.045

Literature

Fat-tailed superspreader events: link

Modelling

We will use a SEISD model: S -> E -> I -> S/D

Where:

• S: susceptable
• E: exposed
• I: infectuous
• D: dead

and total population N = S + E + I

No "recovered" state R is present, because immunity does not last long.

Here:

• beta: infection rate (1/beta: time between infections) S -> E
• a: exposed rate (1/a: period that person is exposed but not yet infectuous, NOT incubation period) E -> I
• gamma: recovery rate (1/gamma: average recovery time) I -> S
• mu: death rate (mu = IFR/T_death) I -> D

The basic reproduction number is then defined as: R0 = beta/(gamma + mu)

The SEIR model uses a more complicated one to account for population growth and normal mortality. However, these can be neglected and thus the R0 reduces to the equation above.

Note that gamma and mu remain largely unchanged. Beta changes because of changes in contact between persons, partially due to the government response. This is reflected in a change of R.

Differential equations defining the model:

Parameters values of the SEIRSD model

Exposure period 1/a (NOT YET INFECTIOUS, average, exponential distribution with parameter a):

• Can't be really determined, let's set it to 2 days for now

Average time of infection 1/beta (serial/generation interval). Generally a day shorter than the incubation time. For Rt = R0 ~ 3, 1/beta ~ 4 days.

• 4.7 days, based on 28 cases, looks like gamma distribution 4-2020 link
• 3.96 days, based on 468 cases 26-6-2020 link
• ~4.1 days, based on 1407 cases 18-6-2020 link
• 3.91 days Italy, 1.81 days China based on SIRD modelling, see saved figure in literature: link

Recovery time 1/gamma

• Time between infection and recovery: 14 days link
• 13.15 days in China, see saved figure in literature (gamma_0 + gamma_1): link

Mortality rate 1/mu

• Not mentioned a lot. Can however be calculated using 1/I dD/dt
  • dD/dt source: link
• See also here though this is a bit old.
• Other source that was sent to me, see also the other figure: link. IFR ~ 0.9% in the Netherlands.
• ~100 days in China after a while link

Background information

Disease model, combination between these two:

• SIRD
• SEIR

Integrator: RK4 Basic reproduction number: link

Other ways of modelling:

• link