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.


Triboelectricity

The triboelectric effect was discovered 2600 years ago by Thales of Miletus. When items in this illustrated (incomplete) list are rubbed together, the low-numbered item gains a positive charge, and the high-numbered item gains a negative charge.

For example, glass rubbed with silk (or, even better, polyester) gains a positive charge, once called “vitreous electricity.” Amber rubbed with wool gains a negative charge, once called “resinous electricity.” Indeed, our word “electron” comes from the Greek ἤλεκτρον, meaning “amber.”


Chemistry can be beautiful: the classic flame test

The flame test occasionally comes up in classic detective fiction: “He snapped off the lights, and we were left with only the sodium flame. In that green, sick glare a face floated close to mine – a corpse-face – livid, waxen, stamped with decay…” (Dorothy L. Sayers & Robert Eustace, The Documents in the Case)

Spectral lines in the image are taken from Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2019). NIST Atomic Spectra Database (ver. 5.7.1), [Online]. National Institute of Standards and Technology, Gaithersburg, MD. Photographs in the image are public domain, from Wikimedia Commons.


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.


A planetary fruit salad

Here is a planetary fruit salad – a scale model of objects in the solar system (click to zoom). The Moon and the smaller planets are on the top left saucer. The lower right saucer represents the rings of Saturn.

On this scale (roughly 1 to 2 billion), the Moon is 19 centimetres from the Earth, the Earth is 73 metres from the Sun, Jupiter is 380 metres from the Sun, and Pluto is around 3 kilometres from the Sun.

Object Diameter Scaled Diameter Model
Sun 1,392,700 km 68 cm Beach ball (not shown)
Mercury 4,879 km 0.24 cm Mustard seed (yellow)
Venus 12,104 km 0.59 cm Chickpea
Earth 12,756 km 0.62 cm Chickpea (coloured blue)
Moon 3,475 km 0.17 cm Mustard seed (black)
Mars 6,792 km 0.33 cm Peppercorn (black)
Jupiter 142,984 km 7 cm Orange
Saturn 120,536 km 5.9 cm Lemon
Saturn’s Rings (up to F) 280,360 km 14 cm Saucer
Uranus 51,118 km 2.5 cm Grape
Neptune 49,528 km 2.4 cm Grape
Pluto 2,377 km 0.12 cm Poppy seed