Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period

Stephen M. Kissler, Christine Tedijanto, Edward Goldstein, Yonatan H. Grad, Marc Lipsitch•View original
OverviewBalancedalloy voice
Picture the moment after that first global shock in early 2020. Hospitals had just weathered their initial surge, and the question hanging over everyone was simple and enormous: what comes next? To know whether we were in for a single crash followed by calm, or a series of rolling waves, we needed to understand immunity. Not philosophically — biologically. How quickly do people make antibodies? How long do those antibodies hang around? And could we use those answers to gauge how much of a city, or a country, had already been exposed? That’s where serology, those antibody tests, became more than a lab tool. They became a compass for the next phase. One of the early compasses was a rapid test from Cellex. Think of it as a tiny chemistry lab on a strip of nitrocellulose. You apply a drop of blood — about ten microliters, so a fingertip amount — and a buffer, and capillary action does the rest. Viral proteins are stuck along the strip, and if your blood has antibodies that recognize them, little gold-conjugated particles pile up and make a visible burgundy line. It’s simple, it’s fast, and it speaks two languages at once: IgM, the early responder, gets its own "M" line; IgG, the later and more durable responder, gets a "G" line. A "C" line acts as an internal control. No control line means no valid test. You wait the right amount of time — between fifteen and twenty minutes — read it, and discard it. Cellex sold these in kits of twenty-five, fifty, or one hundred tests, designed to be stored between two and thirty degrees Celsius, then brought to roughly room temperature before use. The mechanics are basic. The stakes were not. So how well did it work? In early evaluations, pretty well. One pooled analysis reported a positive percent agreement — which you can think of as sensitivity against a reference standard — of ninety-three point seventy-five percent, with a confidence interval from about eighty-eight to ninety-seven percent. The negative percent agreement, a proxy for specificity, landed at ninety-six point forty percent, with a confidence interval from roughly ninety-two to ninety-eight percent. Another summary put those same results in concrete counts: out of one hundred twenty-eight known positives by a comparator method, the test picked up one hundred twenty; out of two hundred fifty known negatives, it correctly called two hundred forty negative. Those numbers don’t shout perfection. But they do say that in the middle of a chaotic spring, a quick read on IgM and IgG could be accurate enough to be genuinely useful — if you understood what it could and could not tell you. When you zoom in on the supporting datasets, the picture holds steady. In one set, ninety-one of ninety-eight samples from people with polymerase chain reaction, or PCR, confirmed infection were positive for IgM, IgG, or both on the Cellex strip. In a pre-pandemic batch collected before September two thousand nineteen, one hundred seventy-four of one hundred eighty samples were negative, as they should be. In a hospital-heavy subset — thirty positive specimens from severely ill patients — twenty-nine registered as antibody positive; among seventy negatives, sixty-five came back negative. And when labs did a kind of reality check by spiking venous whole blood with known positive serum, the strip’s answers matched expectation ninety-nine percent of the time. That’s reassuring because real-world specimens are messy. Blood has proteins and lipids and — frankly — whatever someone ate for lunch. Seeing the test behave across specimen types told labs they could deploy it without a thousand caveats. Specificity — the art of not being fooled — mattered just as much. Cross-reactivity testing ran the strip against a menagerie of antibodies to other pathogens, including a panel of human coronaviruses collected before the SARS-CoV-2 era. In that set, there were no false positives and no false negatives. That doesn’t mean cross-reactivity can never happen; the documentation is careful to say that false positives from cross-reacting antibodies are possible, which is why a positive result shouldn’t be the sole basis for a diagnosis. But it does mean that, at least in the pathogens they checked, the assay’s antigens weren’t indiscriminately sticky. For a public health lab staring down a stack of samples, "no surprises" is about as good as it gets. Timing, though — timing is everything with antibodies. IgM typically appears several days after infection. IgG follows later. If you test someone very early, a negative strip doesn’t clear them; it just means their humoral response isn’t detectable yet. And even when those lines appear, their intensity isn’t a ruler. The test is qualitative. A dark band doesn’t translate to a precise titer, and the makers explicitly warn against reading intensity as amount. Add to that the most important unknown of all in spring 2020: how long do these antibodies persist? The short answer in the documentation is, we didn’t know. Not for IgM. Not for IgG. That single uncertainty, sitting right next to the promise of serology, is the hinge on which long-range projections swing. There’s also the simple reality that a rapid strip has a narrow window of truth. Read it between fifteen and twenty minutes. Not at ten, not at twenty-five. After twenty minutes, you can see "ghost" lines as the chemistry dries out and background creeps in. The control line must appear, or you’re flying blind and need a new cassette. Quality controls — known positive and negative samples — are recommended to track performance over time. And the physical handling matters: store the kits between two and thirty degrees, don’t freeze them, bring reagents to about fifteen to thirty degrees before running a batch. None of this is exotic. But in field conditions — pop-up clinics, mobile units, makeshift labs — the difference between following those rules and not can show up in your false call rate. Now, let’s pull back to the big question we started with: how do these test results feed into projections about the post-pandemic period? A serology strip can tell you, with the performance caveats we’ve walked through, whether someone has mounted an antibody response and whether it looks early (IgM) or later (IgG). Aggregate that across a population, and you get a seroprevalence estimate — a snapshot of how much exposure has likely happened. But there’s a catch. If you don’t know how long IgG sticks around, you can’t convert a snapshot into a movie. If antibodies wane quickly, today’s positive may be tomorrow’s negative, and your estimate of "ever infected" will slide under you. If they persist, today’s snapshot is a reasonable map of cumulative exposure. The Cellex documentation is explicit about this gap: at that time, the duration of IgM and IgG persistence after infection was unknown. That gap matters because the models people wanted to build — the ones asking whether we’d see recurrent wintertime outbreaks, whether distancing could be intermittent, how hard intensive care units might be hit — live and die on a few parameters. Seasonality, which turns transmission up or down over the year. Waning immunity, which controls how quickly the recovered pool drifts back into susceptibility. And cross-immunity, the partial protection you might carry from other coronaviruses. The materials in front of us don’t give those model knobs and dials. They focus, instead, on the instrument you’d use to measure the outcome of a thousand invisible infections. To borrow a physics metaphor, this is the detector description, not the cosmology. That isn’t a bug. It’s how science works under pressure. You build a measurement you trust, you chart its boundaries, and you feed its outputs into whatever can make sense of them. If you were a hospital lab director evaluating whether to deploy Cellex early on, you’d weigh that ninety-three point eight percent positive agreement and ninety-six point zero percent negative agreement against your use case. If you’re screening convalescent plasma donors, that sensitivity might be enough. If you need to rule out past infection in a small, high-stakes cohort, you might confirm with another method. And you’d absolutely tell your clinicians that a single negative in the first week of symptoms doesn’t close the book because IgM can lag and IgG later still. There are a few quiet strengths here that matter for public health, too. The clean cross-reactivity panel — including a pre-two thousand nineteen human coronavirus set — reduces the odds that your seroprevalence estimate is inflated by off-target binding to common cold coronaviruses. The ninety-nine percent concordance when using venous whole blood spiked with positive serum says the assay can handle real-world matrices without melting down. And the logistics — compact kits, no instrumentation, a fifteen to twenty minute read — meant you could stand up testing in places without high-throughput lab gear. Those are not small wins when the alternative is no data. If you’re wondering where the curve-fitting and the equations are, this is the moment to be candid: they’re not in this slice of the record. The projections you’ve heard about elsewhere — the ones that mix seasonally forced transmission with waning immunity and cross-immunity to tell you whether you’ll see biennial peaks or lockstep winters — rest on parameters that aren’t part of these materials. What we do have is the foundation: a way to say, with known uncertainty, who has seroconverted, and when that likely happened in the course of an illness. So where does that leave us? In a place that’s both familiar and honest. Serology gave early pandemic decision-makers a window into past exposure, bounded by the realities we’ve walked through: good but not perfect sensitivity and specificity, biological timing that can elude a single test, and an unresolved question about how long those burgundy lines correspond to protection. You can build policy with that, carefully. You can monitor trends, design follow-up studies, and refine your models as longitudinal data arrive. And if we allow ourselves a brief look forward, the path is clear. Pair rapid serology with longitudinal follow-up to nail down antibody persistence. Align qualitative strips with quantitative assays so a "line present" today can be anchored to a titer tomorrow. And always, always interpret a positive or a negative in the context of timing, symptoms, and other tests. In the scramble to see the road ahead, the Cellex strip was a headlamp. It didn’t tell you where the highway ends. But it lit up the next few meters, and in a storm, that’s how you keep moving.

Picture the moment after that first global shock in early 2020. Hospitals had just weathered their initial surge, and the question hanging over everyone was simple and enormous: what comes next? To know whether we were in for a single crash followed by calm, or a series of rolling waves, we needed to understand immunity.

Not philosophically — biologically. How quickly do people make antibodies? How long do those antibodies hang around?

And could we use those answers to gauge how much of a city, or a country, had already been exposed? That’s where serology, those antibody tests, became more than a lab tool. They became a compass for the next phase.

One of the early compasses was a rapid test from Cellex. Think of it as a tiny chemistry lab on a strip of nitrocellulose. You apply a drop of blood — about ten microliters, so a fingertip amount — and a buffer, and capillary action does the rest.

Viral proteins are stuck along the strip, and if your blood has antibodies that recognize them, little gold-conjugated particles pile up and make a visible burgundy line. It’s simple, it’s fast, and it speaks two languages at once: IgM, the early responder, gets its own "M" line; IgG, the later and more durable responder, gets a "G" line.

A "C" line acts as an internal control. No control line means no valid test. You wait the right amount of time — between fifteen and twenty minutes — read it, and discard it.

Cellex sold these in kits of twenty-five, fifty, or one hundred tests, designed to be stored between two and thirty degrees Celsius, then brought to roughly room temperature before use. The mechanics are basic. The stakes were not.

So how well did it work? In early evaluations, pretty well. One pooled analysis reported a positive percent agreement — which you can think of as sensitivity against a reference standard — of ninety-three point seventy-five percent, with a confidence interval from about eighty-eight to ninety-seven percent.

The negative percent agreement, a proxy for specificity, landed at ninety-six point forty percent, with a confidence interval from roughly ninety-two to ninety-eight percent. Another summary put those same results in concrete counts: out of one hundred twenty-eight known positives by a comparator method, the test picked up one hundred twenty; out of two hundred fifty known negatives, it correctly called two hundred forty negative. Those numbers don’t shout perfection.

But they do say that in the middle of a chaotic spring, a quick read on IgM and IgG could be accurate enough to be genuinely useful — if you understood what it could and could not tell you.

When you zoom in on the supporting datasets, the picture holds steady. In one set, ninety-one of ninety-eight samples from people with polymerase chain reaction, or PCR, confirmed infection were positive for IgM, IgG, or both on the Cellex strip. In a pre-pandemic batch collected before September two thousand nineteen, one hundred seventy-four of one hundred eighty samples were negative, as they should be.

In a hospital-heavy subset — thirty positive specimens from severely ill patients — twenty-nine registered as antibody positive; among seventy negatives, sixty-five came back negative. And when labs did a kind of reality check by spiking venous whole blood with known positive serum, the strip’s answers matched expectation ninety-nine percent of the time. That’s reassuring because real-world specimens are messy.

Blood has proteins and lipids and — frankly — whatever someone ate for lunch. Seeing the test behave across specimen types told labs they could deploy it without a thousand caveats.

Specificity — the art of not being fooled — mattered just as much. Cross-reactivity testing ran the strip against a menagerie of antibodies to other pathogens, including a panel of human coronaviruses collected before the SARS-CoV-2 era. In that set, there were no false positives and no false negatives.

That doesn’t mean cross-reactivity can never happen; the documentation is careful to say that false positives from cross-reacting antibodies are possible, which is why a positive result shouldn’t be the sole basis for a diagnosis. But it does mean that, at least in the pathogens they checked, the assay’s antigens weren’t indiscriminately sticky. For a public health lab staring down a stack of samples, "no surprises" is about as good as it gets.

Timing, though — timing is everything with antibodies. IgM typically appears several days after infection. IgG follows later.

If you test someone very early, a negative strip doesn’t clear them; it just means their humoral response isn’t detectable yet. And even when those lines appear, their intensity isn’t a ruler. The test is qualitative.

A dark band doesn’t translate to a precise titer, and the makers explicitly warn against reading intensity as amount. Add to that the most important unknown of all in spring 2020: how long do these antibodies persist? The short answer in the documentation is, we didn’t know.

Not for IgM. Not for IgG. That single uncertainty, sitting right next to the promise of serology, is the hinge on which long-range projections swing.

There’s also the simple reality that a rapid strip has a narrow window of truth. Read it between fifteen and twenty minutes. Not at ten, not at twenty-five.

After twenty minutes, you can see "ghost" lines as the chemistry dries out and background creeps in. The control line must appear, or you’re flying blind and need a new cassette. Quality controls — known positive and negative samples — are recommended to track performance over time.

And the physical handling matters: store the kits between two and thirty degrees, don’t freeze them, bring reagents to about fifteen to thirty degrees before running a batch. None of this is exotic. But in field conditions — pop-up clinics, mobile units, makeshift labs — the difference between following those rules and not can show up in your false call rate.

Now, let’s pull back to the big question we started with: how do these test results feed into projections about the post-pandemic period? A serology strip can tell you, with the performance caveats we’ve walked through, whether someone has mounted an antibody response and whether it looks early (IgM) or later (IgG). Aggregate that across a population, and you get a seroprevalence estimate — a snapshot of how much exposure has likely happened.

But there’s a catch. If you don’t know how long IgG sticks around, you can’t convert a snapshot into a movie. If antibodies wane quickly, today’s positive may be tomorrow’s negative, and your estimate of "ever infected" will slide under you.

If they persist, today’s snapshot is a reasonable map of cumulative exposure. The Cellex documentation is explicit about this gap: at that time, the duration of IgM and IgG persistence after infection was unknown.

That gap matters because the models people wanted to build — the ones asking whether we’d see recurrent wintertime outbreaks, whether distancing could be intermittent, how hard intensive care units might be hit — live and die on a few parameters. Seasonality, which turns transmission up or down over the year. Waning immunity, which controls how quickly the recovered pool drifts back into susceptibility.

And cross-immunity, the partial protection you might carry from other coronaviruses. The materials in front of us don’t give those model knobs and dials. They focus, instead, on the instrument you’d use to measure the outcome of a thousand invisible infections.

To borrow a physics metaphor, this is the detector description, not the cosmology.

That isn’t a bug. It’s how science works under pressure. You build a measurement you trust, you chart its boundaries, and you feed its outputs into whatever can make sense of them.

If you were a hospital lab director evaluating whether to deploy Cellex early on, you’d weigh that ninety-three point eight percent positive agreement and ninety-six point zero percent negative agreement against your use case. If you’re screening convalescent plasma donors, that sensitivity might be enough. If you need to rule out past infection in a small, high-stakes cohort, you might confirm with another method.

And you’d absolutely tell your clinicians that a single negative in the first week of symptoms doesn’t close the book because IgM can lag and IgG later still.

There are a few quiet strengths here that matter for public health, too. The clean cross-reactivity panel — including a pre-two thousand nineteen human coronavirus set — reduces the odds that your seroprevalence estimate is inflated by off-target binding to common cold coronaviruses. The ninety-nine percent concordance when using venous whole blood spiked with positive serum says the assay can handle real-world matrices without melting down.

And the logistics — compact kits, no instrumentation, a fifteen to twenty minute read — meant you could stand up testing in places without high-throughput lab gear. Those are not small wins when the alternative is no data.

If you’re wondering where the curve-fitting and the equations are, this is the moment to be candid: they’re not in this slice of the record. The projections you’ve heard about elsewhere — the ones that mix seasonally forced transmission with waning immunity and cross-immunity to tell you whether you’ll see biennial peaks or lockstep winters — rest on parameters that aren’t part of these materials. What we do have is the foundation: a way to say, with known uncertainty, who has seroconverted, and when that likely happened in the course of an illness.

So where does that leave us? In a place that’s both familiar and honest. Serology gave early pandemic decision-makers a window into past exposure, bounded by the realities we’ve walked through: good but not perfect sensitivity and specificity, biological timing that can elude a single test, and an unresolved question about how long those burgundy lines correspond to protection.

You can build policy with that, carefully. You can monitor trends, design follow-up studies, and refine your models as longitudinal data arrive.

And if we allow ourselves a brief look forward, the path is clear. Pair rapid serology with longitudinal follow-up to nail down antibody persistence. Align qualitative strips with quantitative assays so a "line present" today can be anchored to a titer tomorrow.

And always, always interpret a positive or a negative in the context of timing, symptoms, and other tests. In the scramble to see the road ahead, the Cellex strip was a headlamp. It didn’t tell you where the highway ends. But it lit up the next few meters, and in a storm, that’s how you keep moving.

More in Mathematics →

Related lectures