In 2020, the COVID-19 pandemic caused many companies to instruct employees to work from home to avoid spreading the disease. Some companies have more restrictive work-from-home policies and still required some presense in a physical office throughout the week. However, COVID-19 infections can largely be asymptomatic for several days while still being contagious and as a result, while an employee may not appear to be sick, they can still infect others for several days before they can self-quarantine.
Under the assumption that you can only pick a few days out of the week to work from home:
- Do more days working from home reduce the time a sick person would be in the office? If so, by how much?
- What would be the best days to be out of the office to minimize the spread of the disease?
This program simulates a 5 day work week, with Saturday and Sunday off. Using incubation period models from recent research which suggests a log-normal incubation time (approximately a mean of 5 days), this program simulates:
- Random day of infection
- Random incubation period from a log-normal distribution
- Length of time an employee would be in the office before symptoms appear
In the simulation, I test several scenarios:
- No work from home (Monday - Friday in the office)
- One day work from home (every combination)
- Multiple days work from home
Each scenario and test combination was tested with 15,000 iterations
On average, a person would spend 4 days in the office before they would realize they are sick (and hopefully self-quarantine)
Below is the summary statistics for a traditional work week (M-F, weekends off)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 3.000 4.000 3.925 5.000 21.000
For comparison, with working from home one day a week (any day), we see the mean time a person is sick in the office is 3.2 days.
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 2.000 3.000 3.157 4.000 16.000
This difference is signifcant at p<0.0001 level.
Additionally, when simulating additional days out of the office, mean time of an employee being sick in the office is reduced linearly by 0.8 days, for each work from home day added.
#0 WFH days
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 3.000 4.000 3.925 5.000 21.000
#1 WFH days
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 2.000 3.000 3.167 4.000 17.000
#2 WFH days
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 1.000 3.000 2.357 3.000 9.000
#3 WFH days
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 1.00 2.00 1.58 2.00 7.00
This question arises due to the idea that you potentially have a longer time out of the office if your WFH day is on a Friday or Monday, results in 3 full days out of the office. This longer period out of the office maybe give an employee more time to develop symptoms outside of work.
In the analysis below, we perform pair-wise t-tests across mean time in the office while sick for each work from home day. The results of the simulation suggest that there is no significant difference in time in the office while sick between days:
Pairwise comparisons using t tests with pooled SD
M Tu W Th F
M - - - - -
Tu 1.00 - - - -
W 1.00 1.00 - - -
Th 0.42 1.00 1.00 - -
F 1.00 1.00 1.00 0.82 -
P value adjustment method: holm
The average time a sick person is in the office is effectively the same across all work from home days.
This simulation shows that for reducing the spread of the COVID-19 virus, working from home can reduce the chances an employee infects their coworkers before they are symptomatic. The more days working from home, the less time an infected employee spends in the office. It also doesn't matter what day you chose.