Field of Science

Thinking about a post-pandemic world

I've been trying to think carefully about what our world will be like once the current pandemic is over.  Most people are rightly focused on the current situation and on short term measures to limit the spread of the virus and the harm it causes, but we should also be thinking about, and planning for, what the world is likely to be like once populations reach some sort of equilibrium.  How many people will the virus be infecting or killing every year?  How much difference will a vaccine really make?  Will we still need to wear masks?

 What follows is my non-rigorous back-of-the-envelope analysis.  I made some big assumptions (spelled out) and did some simple arithmetic of a few simple scenarios.  There's no proper modeling here.

What kind of equilibrium we get will depend on how much immunity develops as a result of Covid-19 infection, how rapidly the immunity fades, and whether or not researchers can develop a vaccine that gives the same immunity.  So first we should consider some very broad-brush scenarios.

These outcomes range from very bad (no immunity, no vaccine) to quite good (lifelong immunity from a vaccine).  But how likely are they?  What kind of future should we plan for?

Based on what vaccine scientists have discovered and accomplished so far, I think that we will get a vaccine.  I also think that both ‘no immunity’ and ‘lifelong immunity’ are so unlikely that we shouldn’t waste time thinking about their consequences.

Now let’s do some planning for the most likely scenario.

Below I add more detail to the most likely outcome, that both infection and a vaccine confer moderate immunity.  I consider the effect of many people refusing (or being unable to pay for) vaccination, and of wearing masks and practicing some social distancing.

Let’s assume that the vaccine is a lot like our current flu vaccine, so it reduces your chance of being infected by about 50%, and your chance of having a severe infection or dying by 90%.  If you do get infected, it also reduces your contagiousness by about 50%.  Let’s also assume that you need to be re-vaccinated every year, both because the immunity fades over time and because in some years a virus mutation makes the current vaccine less effective.

What might the annual Covid-19 infection rates and death rates be in a typical year?  Let’s consider four scenarios that capture the most important possibilities:
  • Scenario A: Many people refuse to be vaccinated (I assume 44% vaccine uptake, like the current flu vaccine), and social interactions return to normal.
  • Scenario B: 44% of people refuse to be vaccinated, as in A. However most people practice some social distancing and wear masks when in crowds, which reduces the number of infections by about 50%.
  • Scenario C: Most people are vaccinated annually, and social interactions return to normal. 
  • Scenario D: Most people are vaccinated annually, as in C.  Most people also practice some social distancing and wear masks when in crowds, as in B., which reduces the number of infections by about 50%.
To estimate how much Covid-19 infection we might expect, I decided to use the CDC’s influenza data (  The CDC estimates that influenza has caused 2,400-14,000 infections and 4-19 deaths per 100,000 people each year since 2010.  So I assumed that if Covid-19 vaccine works as well as the flu vaccine but with poor uptake and social interactions returned to normal, we would have about 7000 Covid-19 infections per 100,000 annually.  Initially I used the current Covid-19 death rate of 1% for unvaccinated people, and 0.1% for vaccinated people.

For comparison here are the extremes of the CDC’s estimates of the current influenza burden, drawn to the same scale:

So, if we get a vaccine that works only as well as the influenza vaccine, but most people get vaccinated, we could have an ultimate Covid-19 death burden lower than the current influenza death burden, even without social distancing and masks.

Some qualifications:

How soon will things stabilize?  Covid-19 is spreading rapidly in many parts of the world, and well controlled in others.  A vaccine like the one I consider will probably be available within a year or so.  It might then take a couple more years for vaccination and infection levels to settle into some kind of equilibrium.  But this will not be even across populations, and local outbreaks will continue to occur, since both vaccination rates and infection rates are likely to differ a lot between communities and between societies.

Covid-19 treatments may get better:  The analysis above assumes that the death rate from Covid-19 infection remains about 1%.  But Covid-19 treatments will probably continue to improve, reducing the death rate in both vaccinated and unvaccinated people.

Covid-19 infections often make people sicker than the flu, and for longer:  The analysis above doesn’t consider the disease burden of non-lethal Covid-19 infections, which appears to be much higher than that of influenza.  Although most people who get the flu feel lousy for a week or less, and return to full health within a few weeks, many Covid-19 infections cause more severe effects, with a wide range of debilitating symptoms that may linger for at least several months.  Because infections in vaccinated people are expected to be much less severe, employers (or insurers) might require proof of vaccination.

It's hard to predict the effects of changing contagiousness:  Above I've assumed that having been vaccinated reduces an infected person's ability to transmit the infection by 50%, and my calculations then assumed that this will reduce the overall number of infections at equilibrium by 50%.  But the dynamics of infection spread are complex, and the actual equilibrium reduction might be much stronger.

Response to Ambur et al.

 The points in purple are objections raised by Ambur et al. to the hypothesis that the main function of DNA uptake by competent bacteria is acquisition of DNA as a nutrient:

These points are typical of those raised when the goal is to dismiss the nutrient hypothesis rather than to carefully consider all the issues.

(i) As yet, there is no clear evidence that the integration of nucleotides taken up by transformation become routed into DNA metabolism.

Yes. Competence has mainly been studied in mucosal commensals, where investigations of metabolism are difficult.  In these organisms absence of evidence is not evidence of absence.

(ii) The presence of exogenous DNA does not appear to induce competence in any transformable species.

Yes, but I don’t see why this is more relevant for the nutrient hypothesis than for other hypotheses.  (Also, Vibrio does use chitin as a signal for competence; its presence indicates biofilms and abundant DNA.)

(iii) Competence in streptococci, like S. pneumoniae, is induced for only a short time period during exponential growth when other resources are highly abundant.

Because laboratory growth conditions for human commensals and pathogens are so different from natural growth conditions, lab cultures are very poor guides to what matters in the real world.  That’s why our work focused on understanding the regulatory machinery.

(iv) Transported DNA is heavily protected against nuclease digestion within the cell, potentially enabling transported fragments to remain intact as a substrate for recombination.

And yet most competent bacteria take up all DNAs they encounter, and DNA that cannot be recombined is efficiently degraded.  The proteins that protect the DNA are also common in non-competent species and so must function outside of transformation.

(v) The hypothesis does not explain why several competent species only take up DNA from close relatives due to conserved DNA uptake sequences (USS and DUS) despite the fact that non-homologous DNA could be used as a source of nucleotides for direct use or degradation.

On the flip side, almost all competent bacteria take up DNA indiscriminately, so DNA’s benefit can’t depend on its information content.  For these exceptions, we have hypothesized that sequence-dependent uptake constraints exist in these species, and have shown that these create molecular drive that causes uptake sequences to accumulate in genomes at frequencies and distributions corresponding to those seen in real genomes with DUS and USS.

Designing better masks

Optimizing design of masks to prevent spread of COVID-19:

(Originally a series of tweets that came out in the wrong order)

1.     COVID-19 is transmitted mainly by droplets and particles in the air we breathe, not by contact with contaminated surfaces.

2.     Surgical and cloth masks only poorly protect an uninfected wearer from becoming infected. 

3.     But these masks CAN reduce virus release by an infectious person, because exhalation produces large wet droplets that are relatively easy to trap on their way out but that rapidly evaporate to smaller dry particles that are hard to trap on their way in (see Wells Curve). 

4.     So the general public should wear masks not to protect themselves from infection but to protect other members of the community, in case the wearer is unknowingly infected. But design of surgical and cloth face masks has not been optimized for this function. 

5.     What properties should such a mask have?
a.     The fabric should block passage of most respiratory droplets.
b.     Most exhaled air should pass through the mask, not around it, even after a cough or sneeze.
c.      Any exhaled air that escapes should escape downward, not upward.
d.     Air and water molecules should pass easily through the mask fabric.
e.     For ease of breathing, exhaled and inhaled air should be filtered over a large area of mask. The mask should not be tightly pressed to the nostrils and mouth.
f.      To maximize air exchange, the mask should not normally enclose a large volume of air.
g.     The space inside the mask should expand in the event of a cough or sneeze, to trap the large volume of air and allow it to be gradually released through the mask (not around it). 

6.     These goals may best be met by long lightweight scarf-type masks that fit snugly around the nose, cheeks and ears, and settle loosely on the shoulders. 

A semi-quantitative framework for long-term thinking about the COVID-19 pandemic

I think the current rush to invoke extreme flatten-the-curve measures needs to be accompanied by careful thought about what we'll do once the measures have had the desired effect.  In particular, how long would restrictive measures need to remain in force, and how will we decide when they can be lifted?  And how can we mitigate the personal, social and economic harms of the measures while they remain in place?

So I've created a series of semi-quantitative graphs to help.  ('Semi-quantitative means that there are numbers on the axes and specific doubling times for periods of exponential growth, but the finer details are rough approximations.)

Here's the tl;dr for the first 6 months:

Points to note:  

  • The Y-axis is log-scale, so small differences in height indicate big differences in numbers of infected people.
  • Five different scenarios are considered, with plausible effects on doubling time of % infected.
  • Restrictive measures are assumed to reduce peak % infected and eventual equilibrium.
  • For all but the most extreme scenario, infection levels remain high (≥1%) even after 6 months.
  • It will be very hard to justify lifting restrictions that have been effective.

Here's the tl;dr if the costly restrictions are lifted after 7 months of misery:

Points to note:
  • In all cases, lifting restrictions makes % infected much worse (remember, log-scale...).
  • The more effective the restrictions were in limiting total infections, the worse the second wave on infection is, and the longer it drags on.
Below are the individual graphs:

If no action were taken (doubling time 3 days):

Infections are assumed to peak at about 30% of the population at weeks 6-10, and then to decline to about 1% of the population since about half of the population will remain susceptible.

If we take actions that have no or low personal cost (doubling time 6 days):
  • Reduce physical contact with other people
  • Don’t touch your face
  • Wash your hands
  • Avoid large groups and crowded places
  • Work from home if this is possible
  • Reduce travel

The peak % infected is lower, maybe 20%,  occurs at weeks 11-16, and declines to about 0.3% provided the restrictions remain in place.

If we take actions that have moderate cost (doubling time 10 days):

  • Cancel pro-sports, concerts, conferences and other large gatherings
  • Close bars and restaurants
  • Cancel university classes

The peak % infected is lower, maybe 15%, occurs at weeks 18-25, and declines to about 0.15% provided the restrictions remain in place.

If we take actions that have high cost (doubling time 20 days):

  • Close all schools and universities
  • Close close non-essential shops and workplaces
  • Close all public buildings
  • Ban all non-essential travel

The peak % infected is lower, about 10%%, occurs at weeks 35-40, and falls to about 1% by week 52 provided the restrictions remain in place.

If we take extreme actions (R0 <1 b="">

  • Lock down the entire population
  • Enforce by police or the National Guard

The % infected slows its increase and begins to decline by week 15.  It continues declining provided the restrictions remain in place.