Coronavirus projections: model 2

Thanks for the positive response to our initial work on a COVID-19 prediction model.  Here are the results of a second iteration in model development.  If you are a Dynochem user, you can also download and run the model from our COVID-19 site.

A challenge with predictions for the outbreak is that we only have reported/ known case data for parameter estimation.  The first model assumed that all infected cases would ultimately be known cases and that detected cases were equivalent to reported known case data.  In our updated model today, detected cases are no longer simply a lag of infected cases but use the fact that a significant portion of infected cases are never reported in known case data.

The fraction that defines this relationship was estimated in recently published analysis of the outbreak in China; using a complex model that included movement between Chinese cities, known cases were estimated to represent only 14% of the total; however they also estimate that the ability to transmit the disease in unknown cases was 55% of that in known cases.  It is difficult to see why an unknown case would be less infectious.  If we assume that all infectious are equally infectious (on average) whether their case is known or not, this leads to an estimate that about 22% of cases are known based on the China data.  We have also taken estimates of the incubation period and infectious period from the China data.

To account for the above treatment of known cases for parameter estimation, the predictive model now includes the following elements:

This is similar to what is known as the SEIR model, except that here the 'Recovered' compartment is split into Isolated and Cured, for the purposes of estimating ICU capacity requirements. We have not included mortality calculations. The concept of known cases (cumul_detected) is linked to the number of infected by the above fraction (test_frac=22%) and the time from test request to test result.  The 5% requirement for ICU beds is 5% of known cases.  Model assumptions are noted on the Process Scheme worksheet together with some notes about possible future changes.  The model includes a Notes tab explaining how to apply it to a specific region.

We have applied the model to both Ireland and Italy today and results are shown below.

Model 2 fit for Ireland data, with timeframe to end March 2020 (Day 0 = February 20).
Curves are model predictions and symbols are observed data.  Plot units are in brackets on the legend.
There is a clear indication of how measures have changed the trend in the numbers Exposed and Infectious.

Potential impact of on/off restrictions in movement for Ireland to end December 2020.  With further limits on people movement [inset], peak ICU needs could be reached in April or June, depending on restrictions.

The (future) predictions in both cases for Ireland and Italy are optimistic in that they assume a further tightening or increased effectiveness of social distancing / restrictions, compared to what we have been able to achieve to date, plus repeated application of those measures for months ahead. There is evidence that Italy has reduced contact to 40% of base level, while Ireland has reduced contact to 50% to date; these levels are indicated by the 'mixing' variable in the model (see inset plots).  The economic and other costs associated with continuation and deepening this regimen (e.g. to 20% or 10% contact) may not be sustainable.  To generate additional predictions with alternative timing and extent of measures, download the model and run this scenario with your own inputs.

Model fit for Italy data, with timeframe to end March 2020 (Day 0 = February 12).
Curves are model predictions and symbols are observed data.  Plot units are in brackets on the legend.

Potential impact of on/off restrictions in movement for Italy to December 2020.  With further limits on people movement [inset], peak ICU needs could be reached around the end of April (day 77 for Italy).  Relaxation of restrictions even for a short period could return demand towards peak levels.

To drill down further and run your own scenarios, download the model and run it.

In addition to challenges interpreting known case data, the number of data available are also limited, therefore model parameters are uncertain and predictions are indicative only.  In particular, the R0 parameter we obtain by parameter estimation to known case data is 3.0 for Italy and 3.55 for Ireland, both higher than values generally quoted for China.  This could reflect differences in social contact patterns, age profile or the importation of cases due to air travel, which are not explicitly included in our model.  Both values being higher than China may be an artifact of having too few data at present and makes the current model predict more severe impacts.