San Francisco’s Three Waves and the potential for a Fourth Wave
My PhD at UC Berkeley was in dynamic systems and chaos theory. For my thesis I watched numbers oscillate and tried to predict their behavior. One macro level view into this pandemic is as a huge dynamic system. I’m using my background, and intuition to look at the previous three waves to make some educated guesses about what might happen in the future. This analysis will miss nuance and at best will only capture the broad trends, but I hope that is sufficient to inform us. There is also the distinct possibility that I will be wrong, but my slogan is that it pays to be pessimistic in a pandemic.
The beginning of each wave
Roughly a year ago I launched this website saying humans aren’t built to understand exponential growth. Here’s my earlier webpage from last year https://www.phoenixdataproject.org/insightyouvsthecurve or listen to this podcast https://www.wnycstudios.org/podcasts/radiolab/articles/dispatch-numbers to help you understand exponential growth. The linear growth of our vaccination campaign cannot compete with the exponential growth of the virus. To win this race with the virus our vaccination campaign has to be very close to the finish line.
Our complacency and underestimation of the virus has launched every wave of this epidemic. I annotated the graph above to show the prelude, launch, and folly of each wave. Using the third wave as a model I’ve included a hypothetical fourth wave.
Our waves up to now
I cut and placed the case curves for all three waves on the plot above. For each wave half of the cases are prior to day 0 and half are after day 0. With the waves defined here are their statistics.
| Statistic | First Wave | Second Wave | Third Wave | Fourth Wave |
|---|---|---|---|---|
| Duration in days | 101 | 128 | 128+ | Unknown |
| Peak Date | April 24th 2020 | August 3rd 2020 | December 25th 2020 | Unknown |
| Launch Date | March 3rd 2020 | June 12th 2020 | October 18th 2020 | Some time in April? |
| Total Cases | 2949 | 9033 | 21603 | 51000 est |
| Total days of hospitalization | 9119 | 10037 | 16978 | no estimate |
| Total Deaths | 58 | 108 | 262 | 60 est. |
| Days of hospitalization per case | 3.09 | 1.11 | 0.79 | no estimate |
| Deaths per Case (mortality rate) | 2.0% | 1.2% | 1.2% | 0.12% est |
| Lag between case peak and hospitalization peak | 2 days | 11 days | 13 days | no estimate |
| Lag between the case peak and peak in deaths | 8 days prior | 37 day lag | 15 day lag | no estimate |
Things to note: from and about the waves.
Each wave started from a higher point and became 2.5 to 3 times bigger than the previous wave. From this I’m estimating that the next wave could be 51k cases.
The mortality rate was remarkably consistent in the 2nd and 3rd waves. The good news is that I expect a much smaller mortality rate in the 4th wave because lots of our most vulnerable population has been vaccinated. Let us say 10 times fewer people die then that means roughly the same number of people die in the 4th wave as died in the first wave.
Hospitalization days doesn’t count the number of individuals hospitalized it counts the number of days a hospital bed was occupied by someone with COVID-19. So if one person was in the hospital for 1 week that would be a total of 7 hospital days for that 1 person.
I don’t know how to predict what’s going to happen with hospitalizations for the fourth wave. I’m sure the hospitalization rate will be less I just don’t know how much less.
The acceleration phase of the 4th wave.
If you look at the start of the second and third waves, their initial trajectories were remarkably similarly to each other. I describe below what might make the fourth wave’s acceleration faster and what might slow the rise.
Why virus growth could be slower.
Vaccines- If our population was closer to fully vaccinated, then the acceleration of the fourth wave would be slower. Unfortunately I suspect only 1/4 of our population will have a minimal amount of immunity by the time the fourth wave starts to accelerate. To make this estimate I am looking at the number of people who are just getting their second dose. These people do not have full immunity but have enough time from their initial shot to have some initial immunity.
Test to Community Care- If we had truly effective testing, tracing, and supported isolation citywide, that could make a dent in the pandemic. Unfortunately this effort is still catch as catch can. The Unidos en Salud model is wonderful but it is being funded by private donors and not being pushed out citywide. Furthermore if the fourth wave is big then this effort would have to be absolutely massive and San Francisco does not seem to have the appetite for that sort of commitment.
Why virus growth could be faster.
New variants- The B.117 variant is spreading incredibly rapidly throughout the rest of the country. There is no reason to think that it won’t spread like wildfire here. Britain a country ahead of us in their vaccine rollout is really struggling to control the B.117 variant.
Reopening speed- The speed with which our community liberalizes and continues to liberalize our socialization strongly affects the trajectory of this virus. The more socialization and reopening that happens the more upwards pressure there is on the curve. When mass gatherings at 20% and 33% capacity are on the near term horizon that is an extreme amount of upward pressure. Once large mass gatherings are taking place then we are sure to get to a point where the virus is growing and growing quickly. I think mass gatherings should only start once we’re coming very close to herd immunity.
My Outlook- near term storm, long term clearing.
I am optimistic for the long term. With the vaccines being rolled out and adapted to the variants I do see a way out of our pandemic. I had just hoped to avoid one last rollercoaster ride. Even delaying some openings by a month or so could do a lot to dampen the rise of the fourth wave. I hoped our government could soft land this epidemic but it looks like there is going to be some turbulence ahead.