Show daily ratios for countries with more than 10000 cases, smoothed with a radius of 2 days:
Include all countries with more than 5000 cases:
Find the mean daily ratio across countries with more than 5000 cases:
Find the mean daily ratio across all countries reporting cases:
Find the mean across all countries, with the values for each country starting with the country first reported more than 50 cases:
Average over countries with more than 5000 cases, but do not take the mean across days:
Average over all countries reporting cases, but do not take the mean across days:
We wanted to understand the seemingly linear decrease in average daily ratios.
Find the linear term in a fit of the first 30 days of the data:
This corresponds to change of average daily ratio with a slope of about 1 in 111 days:
Summarizing Country Daily Ratio Data
Show daily ratio by country, together with the average over all reporting countries:
Include only countries with more than 5000 cases reported:
Compare results for all countries, and countries with more than 5000 cases:
Show results successively dropping certain countries:
Show how many countries are included in the averages for each day, including only countries with more than 5000 current cases:
Show how many countries are included in the averages for each day, including all countries reporting cases:
Possible Model for Results
In the standard SIR continuum epidemiological model, the number of infected people is i[t], and there is a “force of infection” β.
Solve assuming an infinite supply of susceptible people, and fixed force of infection; the result is a pure exponential:
Solve assuming a force of infection that varies linearly with time:
A typical model is that the distribution of times between becoming infected and showing symptoms is an exponential distribution.
Show the PDF for an exponential distribution:
The ratio of successive values will be given roughly by the log of the PDF:
More accurately, it is the ratio of PDF to CDF:
The continuum SIR model does not accurately represent human contacts, especially when they are limited by social distancing. It is better to consider a network, although it is not clear what the correct network should be.
Generate a typical example of network that models certain features of human networks:
At larger scales, human networks will tend to reflect actual geographical (i.e. spatial) relations, and so will have features of random planar networks.
Generate an example of a random planar network:
Make larger examples of these types of graphs:
For the model human network, the graph diameter is still quite small:
Starting from one node in the graph (i.e. one person) this shows the number of nodes reached after n steps in the random planar graph:
Data from Actual Contagion Networks
Singapore has carefully tracked cases, and generated a network giving information on contagion.
Import the data:
Show the network from this data:
Find cases of person-to-person transmission, giving the case numbers involved:
Plot case numbers for transmission pairs:
This data seems to indicate that most transmissions are found by backtracing. The analysis should be repeated with actual report times included.
Analysis of Government Responses
Import a dataset of measures implemented by governments:
Show counts of measures implemented:
Show a word cloud of measures taken:
Show a date histogram of when measures were implemented:
Show a histogram of when the first measure was implemented for each country:
Show a histogram of the average time when measures were implemented:
Compute when general lockdown was implemented in each country:
Find how many countries have implemented general lockdown so far:
Make a histogram of when general lockdown was implemented:
Comparing with Cases
Compute when each country first reported more than 100 cases:
Make a date histogram of when more than 100 cases were first reported:
Compare when countries first implemented measures vs. when they first reported 100 cases:
Compare the average of when countries implemented their various measures vs. when they first reported 100 cases:
Compare the difference in time between reporting 100 cases, and the first measure being implemented:
Compare the difference in time between reporting 100 cases, and the average of when measures were implemented: