Some principles of network epidemiology

Lockdowns and “flattening the curve” are very much in the news right now, so I thought it was timely to post about some principles of network epidemiology. The charts below (click to zoom) show the simulated spread of a disease (in a small “toy” population of 2000) subject to certain assumptions. The blue lines show the total number of cases over time (adding up those infected, recovered, and dead). This total number is important because some percentage of the final total will die, and we want to minimise that (if we can). The red lines show the number of current infections over time. This is important because some percentage of the red numbers are in hospital, and the red peak therefore represents peak load on the medical system.

In the top row, we have connections happening at random, with increasing social distancing happening from left to right. Moderate social distancing doesn’t change the fact that almost everybody gets the disease, but it does delay and reduce the peak, thus taking strain off the medical system. Extreme social distancing saves many lives, but only if social distancing is continued for a long time (in real terms, until a vaccine is available, which is almost certainly not sustainable).

In the middle row, we have the same number of contacts happening as in the top row, but most of the contacts are within limited social circles. Such contacts, between family members and close friends, are less serious than contacts with strangers. If Peter is your close friend, and you catch the virus, then there’s a reasonable chance that Peter caught it the same way, and so there’s a reasonable chance that your contact with Peter makes no actual difference. If Peter is a spouse, child, or flatmate, that’s quite a good chance. Contacts with strangers, however, can spread the disease from one social circle to another, and so are far more serious.

In the bottom row, we again have the same total number of contacts happening, but a few “super spreaders” have many more contacts than average (while the majority have slightly less than average, to compensate). This third scenario is significantly worse than the top row – higher, earlier, red peaks, and many deaths even when there is extreme social distancing. Unfortunately, experience has shown that medical personnel, in spite of the fantastic work that they do, have the potential to be serious “super spreaders,” because:

  • they have contact with many patients;
  • the patients are strangers; and
  • the patients are more likely than average to be elderly and/or vulnerable.

This is why personal protective equipment (PPE) for medical personnel is so critically important, as are good testing protocols for medical personnel. Other kinds of “super spreaders” also occur, of course, and it is important to identify them, test them, and provide them PPE (or stop them doing what they’re doing, if it’s non-essential – some jurisdictions with supposedly strict rules are still allowing prostitutes to operate, for example).

Overall, if we look at columns in the picture (all three charts in each column have the same total number of contacts), we see that the kind of contact is just as important as the number of contacts. Isolation regulations in some jurisdictions don’t always recognise that fact, unfortunately.


Coronavirus diary #1

The SARS-CoV-2 coronavirus is changing the world. Ridiculous and selfish panic-buying is stripping supermarket shelves, in Australia as elsewhere. Everyone I know is catching up on their reading, and people are being persuaded to practice social distancing and to wash their hands.

It seems to me that if you’re under 50 and healthy, there is absolutely no need to panic. But it’s really important not to pass on the disease, if and when you catch it, to other people. Listen to your local medical advice, people!

Virus photo from NIAID Rocky Mountain Laboratories; supermarket photo by Christopher Corneschi, 9 March 2020; painting by Marguerite Gérard; hand-washing photo by Michelle Gigante/USAF.


The spread of the COVID-19 coronavirus

Above is a chart of worldwide cases of the COVID-19 coronavirus disease (data from here, skipping the first few days). The apparent spike in cases on February 12 is due to a change in how cases are diagnosed and reported.

There does not seem to be the exponential growth in cases that one would expect (see the badly-fitting blue curve), except at first. In fact, allowing for the “false spike,” growth seems to be almost linear (see the dashed purple line). This would probably be due to under-counting (the Chinese medical system can only diagnose a certain number of cases each day), although it offers some hope that quarantine measures may be working. Let us pray that they continue to work.