Can You Safely Go Out?
I wanted to know: If I go out, how likely am I to get infected with coronavirus? I figured it out. You can, too. Read about it, here.
Every morning, people wake up in the middle of this coronavirus pandemic, and ask: is it safe for me to go about my business today? What information is available to me, to make that decision? Are the public health officials going to save all lives?
The public health officials of most communities - cities, states, countries - provide a few numbers to answer these questions: typically, the number of “new cases” (loosely defined as the number of newly diagnosed covid19 patients, typically but not always via a DNA-swab test), the number of “new hospitalizations”, and the number of “new deaths”.
Most often, people are not reacting to those numbers; they’re reacting to the guidance given them by the executive leader - the governor, the premier, the President, the Prime Minister, the mayor - who declares the public health emergency; the “shelter-in-place” ruling; who is an emergency worker, an essential worker; who can go out, for how long, for what purpose.
And as the epidemic proceeds in our communities, the most stringent of restrictions are being lifted, by these same executives.
But, based on what? These numbers don’t have any informative transparency. We’re reliant on the advice public health officials give these executives, and that these exeuctives follow that advice — and they don’t always do so.
Why can’t a better rubric for understanding these rules be provided?
I live in Montreal, my beloved partner lives in New York City, and I have connections elsewhere, like Switzerland, Chicago, California, and so on. At various times during the epidemic, different executives would declare various types of shut-down. Early on in the epidemic, the number of cases, and deaths, were simply growing exponentially, on timescales of 4-5 days. Whether or not an executive declared a shutdown, largely depended on if they believed community transmission had taken hold — where individual case management became impossible, and tracking down contacts of the newly infected could no longer be feasibly done. Eventually, nearly all communities were in some form of executive-enforced lock-down/stay-at-home order.
But now, months later, the peak of the infection rates have largely passed; the exponential growth is, for many communties, a thing of the past, and we see case rates and death rates have stablised, or are slowly decreasing, on timescales of 20 days, and longer.
I wanted a method of seeing just how likely I would be to become infected, assuming the situation we have today continues on for the forseeable future.
I found I could calculate, using the commonly provided new case rates and new death rates, the amount of time it would take, from today, for me to become infected with coronavirus.
Mean Half-Time to Infection
To examine the risk of infection on both a personal and a population level, I calculate the Mean Half-time to Infection (MHTI). This is the amount of time, from any given day, for a typical person in a given population to accrue approximately 50% chance of becoming infected with coronavirus. It is also the amount of time for 50% of a given population to become infected with coronavirus. I wrote up a longer description of this, where you can find full details, and an example calculation, using Switzerland’s data.
This is a value which I can compare, between different communities; I could examine what steps were taken in France at one given MHTI, and compare what steps were taken elsewhere at the same MHTI. In short, the MHTI empowers me to determine if the steps taken by my government, and those taken by others, are consistent in severity with one another, based on the real risk of a population-wide infection — or if they are possibly more arbitrarily taken, or less informed by public health officials - assuming that public health officials use some similar measure of risk of infection to the population.
Based on those comparisons, and the MHTI for the communities I live in, I can see if the advice local officials are giving, is in line with that given in other communities. I’m sort of surprised, that we seem a lot more reckless than I think we should be.
You can think of this as just another way of looking at the per-capita New Cases Rate (where we must also assume a number of infections per case), or at the per-capita New Deaths Rate (where we must also assume an infection fatality rate - the percentage of infections which result in fatality).
Throughout this discussion, we assume the number of infections per case to be 10; and the infection fatality rate to be 0.66%. See the above link, for discussion on uncertainty in those values, and their effect on the MHTI.
7-day Average Daily Death Rates: Switzerland, NYC, Quebec (including Montreal), Chicago, Montreal
We look at data from Switzerland (pop 8.6M), NYC (pop 8.5M), Quebec (including Montreal: pop 8.5M), Chicago (pop 2.6M) and Montreal (pop 1.8M). The data are taken from various sources, as far back as available (generally after March 1 2020), up to the first week of June 2020. If you want to look at any of the data, data sources, graphs, and calculations behind all of this, you can find them here.
There are two important corrections to the data from Montreal. On May 3, Quebec health authorities announced that over 1000 new cases which should have been included in the April data, were not, and these were added in a batch on that single day. On May 31, Quebec health authorities announced that over 100 new deaths which should have been included previously (dates unspecified), and these were added in a single batch, on that day. Thus, those dates are excluded from trailing averages in their respective datasets, except for the day of correction.
The trailing 7-day average daily death rates are shown below.
Switzerland and NYC both exhibit similar death rates as a function of time. They show an initial exponential rise (typical exponential timescales for the rise were 4-5 days); then, public health measures (such a sheltering-in-place and social distancing) arrested that rise, resulting in an eventual peak in death rates. The timescale for fatalities, following an infection, has been measured between 20-25 days after infection, and that’s what results in the long tail to the death rates, after the peak - seen in both Switzerland and New York.
Quebec (including Montreal) fatality rate tells a different story. While it does display an initial exponential rise, it does not peak and then drop off - instead hitting a maximum and staying at an approximate constant for almost a month (April 21-May 17). Then, instead of exhibing a 20-25 day timescale decay as seen in Switzerland and NYC, there is a drop of about 30% in the death rate, from May 15-May 21, at which point the drop ends, and the deathrate either stays constant, or slightly increases through the first week of June.
Chicago, in contrast, shows an extremely slow climb in death rate (March 29-May 10), rather than an exponential one; this indicates the effects of public health interventions to suspend the expected exponential rise of a pandemic were only weakly effective, simply decreasing the infection rate enough to slow the exponential timescale, and delaying the peak in death rate to May 10). This indicates that interventions from ~20-25 days earlyer (on or about April 20th) in Chicago had the needed impact to most dramatically slow the infection rate, such that the death rate would begin to drop, as it did, by 50% over the month of May, through the first week of June.
Mean Half-Time to Infection for Switzerland, New York City, Quebec (including Montreal), Chicago, Montreal
The MHTI for a population can be calculated two ways: (1) using Daily New Cases only, plus assumptions; or (2) using Daily New Fatalities only, plus assumptions. Which one is more reliable, may depend on the community. Perhaps in one community, testing is poor, so the case rates are dramatically underestimated (and the MHTI overestimated); or, they are failing to register all deaths as due to covid19 if, for example, they take place anywhere but in a hospital (and, again, the MHTI is overesimated).
Moreover, the date attached to each value is the date of reported death, taking an average over the trailing 7 days. The MHTI “from Cases”, because diagnosis follows infection by a median ~6 days, is a lagging indicator of the infection rate 6 days earlier; likewise, the MHTI “from Deaths”, because deaths follow infection by a median 20-25 days, is a lagging indicator of the infection rate 20-25 days earlier.
I’ve discussed Switzerland’s MHTI in detail previously, so I refer you there. But on this log-linear plot, we can see how the MHTI “from Deaths” (blue line) drops linearly from 100 years to 1 year, between March 8 and about April 1. Then, the MHTI increases linearly from 5 years to 50 years from May 5 to May 31st. This means, in Switzerland, the MHTI was so long by 20 days before 31st (about May 11) that it would take a typical person in Switzerland about 50 years, assuming all conditions remain the same, before they become infected. This is a low rate of infection for both public health and personal considerations.
New York City’s MHTI “from Deaths” indicates a similar process as Switzerland; however, the MHTI bottomed out near ~0.25 years between April 5 and April 19th (indicating that the MHTI was shortest ~20-25 days earlier (between about March 15 and April 4th; I’m going stop referring to the period of infection rates the MHTI “from deaths” refers to at this point, and refer only to the MHTI as measured on a particular date, leaving it to the reader to subtract off the 20-25 days. Also, this seems a good place to remind the reader: uncertainties in the infection fatality rate are about a factor of 2, which puts a corresponding factor of 2 uncertainty in the MHTI). Nonetheless, thereafter, the MHTI increases linearly (on this log-linear plot) from April 19 to June 4, at which point the MHTI is about 3 years.
Quebec’s (including Montreal) MHTI “from Deaths” was, in the last week of March, still high, near 100 years. It then decreased sharply over April, until April 19, when the MHTI was ~1 year. Here is a key point: From April 19 for the following 6 weeks, Quebec’s MHTI has remained nearly constant - about 1 year. It shows no sign of increasing, as it should if public health interventions are suppressing the infection rate. It seems clear that the coronavirus infection rate, based on the fatality rate, is not decreasing in Quebec, since April 19.
Chicago’s MHTI “from Deaths” show that Quebec is not unique in this regard; in early march, Chicago’s MHTI was >100 years, decreasing to <1 year by April 5, bottoming out near 0.5 years in early May, and then increasing to between 1-2 years the first week of June, still only slowly increasing.
Statistics from Montreal’s early days are sparse; but Montreal’s MHTI was >10 years until late March, and dropped to <1 year around April 6th; the MHTI was close to 0.25 years between April 19-May 17, and at last began to increase, and is now just above 0.5 years, in the first week of June.
As explained in the above referenced document where I describe calculating the MHTI, all these MHTI numbers have uncertainties of ~2 (they may be half the calculated value, or double the calculated value), systematically, due to the uncertainty in the infection fatality rate.
Even so, it’s clear to me that Montreal’s MHTI is very short, certainly compared to Switzerland, and even to New York City, meaning a person is more likely to be infected here, going about their normal business, even under the present lock-down conditions, than in Switzerland or New York City, under their conditions. Moreover, the MHTI from deaths is a lagging indicator, since it is a measure of the infection rate 20-25 days before; but Montreal went into a limited “re-opening” just 18 days ago, on May 20th; we have yet to see what the increased levels of public interaction will do to the infection rate and subsequently the death rate - but it seems reasonable to expect that both of these will increase, and the MHTI will even go down again.
The prognosis does not seem good. As a denizen of Montreal, it seems to me that, today, Montreal is no less infectious than it was in early April, when the city was more or less in lock-down, with all major businesses and public accommodations closed. That we began, at the behest of the provincial government, a “re-opening” of non-essential businesses, public gardens, various public sporting areas, museums, parks, and more in late May, does not seem, to me, to be informed by the level of infectiousness of Montrealers.
At best, it seems the city is following the dictum: “Re-opening does not mean that you will not be infected, it means there is room for you in the ICU”.
Having kept the public health institutions intact, it seems decisions are being made which would allow these institutions to continue to manage the current level of infection, without collapsing — rather than to save all lives.
Questions to ask your public health officials
Regardless of where you live, your public health officials should be able to explain:
What is their calculation of the Mean Half Time to Infection, and how has that been used in planning “re-opening”?
If public health officials in your area have not previously discussed the likelihood that a citizen becomes infected, but rather focus on the load on our healthcare system, they should explain how the goal of saving all lives — and not just saving the health care system, which is a less stringent requirement — has informed their decision making for re-opening.
In the absence of any vaccine or effective treatment, is your community’s plan to allow as many people to become infected, at only a low enough rate that health institutions can manage the sick and the bodies of the dead? Why not, instead, lock down until the infection rate goes to zero — such as in New Zealand, and South Korea — and save all lives?
Reference
The data used, the calculations performed, and the plots which resulted and are used above, are given and described in this spreadsheet.