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Pre and Asymptomatic Spread

Pre-symptomatic and genuine asymptomatic transmission seems to be a reality with COVID-19. People who are pre or asymptomatic typically act in the same way as non-infected people, whereas symptomatic people will either self-isolate, be quarantined or be hospitalised.

The solution is yet more compartments. This time we'll put pre clinical after exposed and split infectious into asymptomatic and symptomatic compartments.

Lockdown Suppression

During a stay at home order the number of people an infectious person can infect reduces significantly from say 3 to 2 to 1 over a relatively short period of time compared to normal. This is modelled by splitting household and non-household transmission, and applying a limit to household transmission such that the number of people infected in their household can never exceed the average household size minus one times the number of people infected out of the home. This is not standard but details available here for examination.

Stages within a compartment

There's a little problem with one box for all. While the average time spent in a box is what we have set it to be, there is a very broad range. The longer the average time in the box, the bigger the range of possible times. To work around this, and match up with the range of times we observe in reality, we can split the compartments into a number of smaller internal boxes which people pass through.
To explain this is a bit more detail, suppose the average amount of time in a box in 7. Then the range of likely values will be from 0 to 21. So if the reality is close to this then one box is a good idea. But what if the range is less. If we split the box into two boxes each of 3.5 [and with ranges 0 to 10.5], then time spent in the two boxes is still 7 on average, but the range would be 1 to 17 [the time spent in one box is not directly related to the time spent in the next box, just like rolling a dice twice is unlike to give the same result]. With 50 boxes you can reduce the range to 5.5 to 8.7 days.
This isn't that important looking at a disease in a historical context [where the average will be fine], but when trying to map day to day changes these stages are important.

Other model variables

    Symptomatic Detection Rate: What fraction of symptomatic is your country trying to test. 1 for everyone, down to ~0.15 for hospitalisations only
    Asymptomatic Detection Rate: What fraction of asymptomatic is your country trying to test/include in reports. 1 for everyone, down to 0 for none [most countries]
    Days from Symptoms to Positive Test Report: This seems to be between 5 and 6 for countries who focus on symptomatic testing
    Future Days to Predict: How far do you want to push it
    Changes: The date of social changes, and there effect on contacts. If lockdown suppression is checked then a minium number of non household contacts for asymptomatics needs to be provide.
View the model and data>

What's not dealt with

I haven't included any of the following features, for the reasons outlined below:

  • Age profile - relatively easy to add, but too many variables to run on your browser.
  • Regional spread - important, but requires far more computing power.
  • Vaccination - easy to add, but in principle vaccine equals end in sight [assuming sufficient uptake and coordination if the duration of immunity is short].
  • Travel/importation of cases - hope to add this soon.

Your national and regional government modelling teams will have lots of data on level of hospitalisation, regional spread, age and gender profiles, census data on workplaces and travel patterns which will help them plan for future changes to social restrictions.

The above models are only suitable when you have a large population. The national and regional governments are probably also using a more individualistic based model, which requires more computer power, but more closely matches the outcomes in clusters in smaller closed populations, like hospitals and residential care facilities.