Waves of Pandemics

Disclaimer: I’m an epidemiologist but NOT a modeler. I leave the real models to the epi model experts. I also am lousy at graphics. The following is meant to be a simplistic way to describe the anticipated waves of COVID.

I posted on Facebook:
Here are two pandemics. There have been two more in the last century (1957 “Asian Flu” and “1968 Hong Kong Flu”). They have followed a similar pattern.

Pandemics come in waves, with the second wave usually bigger than the first, and with marginalized communities being most impacted in the second wave. We’ve spent a lot of time talking about “flattening the curve.” But we’ve ignored the second wave that will no doubt come without control measures.

While the second wave of the 1918 pandemic was due in large part to a new variant of the flu virus (which is not likely the case for SARS-COV-2), the pattern we see in an outbreak is consistent across pandemics.

The question was asked, so where are we with COVID? How long until the next wave? What factors lead to that second wave? Note in both flu pandemics, cases decreased in summer months. Some of this may have been due to schools being out of session — children with flu are highly contagious (not sure yet how kids play a role in COVID-19). Some of it may have been due to people being more out of doors in summer. In South Texas (where people are often not outside in Summer), that “valley” in 2009 wasn’t quite so low as it was nationwide.

Back to the models. This isn’t intended to be a definitive model, just an example of what COVID could look like.

The incubation period is 2- 14 days. The median number of days after exposure that someone feels sick is 5 days. Most people will be sick by 9–10 days, but there are a few outliers.

A person can be contagious a day or so before they develop symptoms. Most people will be MOST contagious at day 5 after they develop symptoms. That’s when their viral load — the number of infectious viruses — is highest. But they can be contagious before Day 5 and are usually contagious a few days after that peak viral load.

Infectivity though, depends not just on the virus but on the environment. Are they in a crowded house? Are they mostly outside? Are they sharing food?

Here’s a scenario of one person exposed yesterday, May 2. He isn’t sick and doesn’t know he was exposed. He had mostly been staying home but had gone out to do some errands on May 2. On May 9, he and a friend decide to go out for dinner at their favorite restaurant, now open. The staff followed all recommended precautions, but the two friends shared a small table eating their meal. The next morning, May 10, he woke with a fever and cough. He was feeling fine the day before, but he was one of those who is contagious before symptoms develop.

Assuming an R0 = 2 (it is anywhere from 1.5–3.5, but let’s go with two for ease of my poor diagramming skills), he infected his friend on May 9. On May 11, his girlfriend visited to bring him food.

Our friend infected on May 9 developed symptoms 7 days later, but they were so mild he hardly noticed. One of his contacts was already immune, so the infection stopped there. But though he was feeling a little cruddy, he went to work in his shared office. Just a little cough, nothing to worry about. Probably allergies. And his co-worker was exposed on Day 12.

And so on.

Each person’s path to symptoms will vary. They may have symptoms on Day 5, Day 9, Day 12. They may be contagious on Day 4, Day 8 or Day 12. If they isolate, they could prevent most of those exposures (household exposures are harder to stop).

Our index case was tested on May 11 (one day after he developed symptoms). Within a month, this one case led to at least 16 new cases. Fortunately, a few exposed individuals were already immune, slowing the spread.

Now, say we have 800 people currently infected and not yet recovered. About 150 of them are in the hospital (so not exposing others in the community). Say of those 650 not in hospital, half are isolated at home with minimal to no contact with others except to bring food (and household contacts are taking very careful measures). That leaves about 325 people still infected, some are at home but have a shared bathroom with their four other family members. And let’s say half of them have such mild symptoms, they go on about their lives. About 1–3% of the population is already immune (hopefully!) so that slows things a bit.

That leaves 150–250 people likely to expose at least two other people in the next 10 or so days. And then 4–15 days later, those new cases expose more.

So when will the second wave appear? If we do nothing — no case finding (contact tracing), no isolation, go to work, go to shops, that wave will come sooner and be higher. My non-mathematical prediction, based on our local environment (we’re all going to be inside with a/c by next week as temps top 100F), a second wave is likely to hit by late July or August.

If we can limit the number of exposed by isolating infected individuals and identifying their contacts, to in turn test and isolate them, we can turn that R0=2 down to R0=1. It’s likely higher in households where people are in close contact and may be closer to R0=3 or 4 in some areas.

We can restart businesses and protect public health, but everyone has to work together (6 ft apart) to make this work. To stop the second wave from becoming a tsunami, we need extensive public health infrastructure AND extensive cooperation and support from the community to follow appropriate physical distancing guidelines.

For additional reading on pandemics and waves:

SARS outbreak was stopped quickly, but we still saw two waves.