Coronavirus (COVID-19) is here, and it is essential to slow the spread.
A very simple model, which is by no means correct, can however still illustrate the importance of reducing number of contacts in order to slow the spread of a virus.
Start input:
- Number of people in the population (example: Denmark: 5.800.000)
- Number of initially infected people (example: 1)
Model parameters:
- Number of people in contact with infected person, on average (example: 5)
- Probability of infection for a person in contact with infected person (example: 10%)
- These values for the model parameters fits such that Denmark went from 1 infected on February 27th 2020 to around 400 infected on March 11th 2020.
And then I created a simple Google Sheet, which calculates the new number of infected persons, one day at a time:
Explanation of the model, and the columns in the spreadsheet:
- A: Day: The date, one day at a time
- B: Population: The total population (constant)
- C: Has or has had virus: People who currently have or have had the virus
- D: Has not had virus: People who have not had the virus (D = B - C)
- E: Has virus: I assume that the virus lives for 14 days in each infected, so it's the sum of H for the last 14 days
- F: Number of people who is in contact with virus (F = E * Contacts per infected)
- G: Number of people who has not had virus, and who is in contact with virus (G = F * D / B)
- H: Gets people: Number of people who gets virus that day (H = Infection rate * G)
Very simple. And here is a chart of infected as time goes by:
It is seen that there is a peak in the number of people that has the virus at the same time.
I'm totally aware, that the model is not correct, and lacks things like not all people can get infected. However, I find the model interesting in the fact that, by changing the number of contacts per infected, I can see the impact on how many people get infected in total, and when the infections peak.
So, in this model, by reducing the average number of contacts per infection from 10 to 5, the peak date is delayed by two weeks.
The morale of this model, is just the same as the experts and politicians keep telling us:
- We need to delay this as much as possible.
- And we delay it by reducing contacts (low number for contacts per infected in this model).
- And of course we need to have a good hygiene as well (low number for infection rate in this model).
