0.13 Reinfections Halve Your Risk of Catching RSV Again

For respiratory viruses like RSV and influenza, each infection leaves a lasting mark—not just on the immune system, but on the very pattern of who gets sick, and when. A new study reveals that over a lifetime, reinfections don’t accumulate at a steady pace. Instead, they follow a predictable, wave-like trajectory shaped by immunological memory—so precise it can be described with a single mathematical equation.

The most striking finding? After just 0.13 reinfections, the risk of catching respiratory syncytial virus (RSV) again drops by half. For human coronaviruses, it’s even less: 0.02 reinfections. These aren’t rounding errors—they’re biological signals. They mean that a single bout of illness can dramatically reshape future infection risk, especially in early life. And across eight major seasonal viruses, this pattern holds: the more you’ve been infected, the slower you accumulate new ones, not linearly, but exponentially. This isn’t random noise. It’s a traveling wave of immunity, marching through time and age, visible only when you stop treating all infections as the same.

The Science

For over a century, epidemic models have relied on frameworks like SIR (Susceptible-Infected-Recovered) to predict how diseases spread. But these models have a blind spot: they treat reinfections as interchangeable with first infections, erasing the history that makes each person’s immune response unique. Whether someone has never been infected or has had five bouts of flu, classical models often assume the same risk of reinfection. That simplification works for acute outbreaks, but fails for pathogens that circulate seasonally and reinfect throughout life—like influenza, RSV, or the common cold.

Piergiorgio Castioni, Chiara Poletto, and Alex Arenas tackle this gap with a new model they call the "chain SIR" (Castioni et al., 2026). Unlike traditional models, it explicitly tracks how many times individuals have been infected, indexing compartments by reinfection count: $S_i$, $I_i$, $R_i$ for those with $i$ prior infections. This creates a “ladder” of immunity states, where each rung represents a new infection.

The model allows key parameters—transmission rate $\beta_i$, recovery $\gamma_i$, and waning immunity $\delta_i$—to depend on $i$. This captures the idea that immune memory builds (or sometimes backfires) with each exposure. From this detailed system, the researchers derive a simplified reinfection flow equation:

$$\frac{\partial N(x,t)}{\partial t}=-\frac{\partial }{\partial x}\left(\sigma (x)N(x,t)\right)-\mu (x)N(x,t)$$

Here, $N(x,t)$ is the fraction of people with $x$ cumulative infections at time $t$, and $\sigma(x)$ is the reinfection rate—how quickly someone with $x$ infections acquires another. The equation describes a traveling wave in reinfection space: as time passes, the population “flows” up the reinfection ladder, but at a speed determined by $\sigma(x)$.

This is not just metaphor.

shows this wave in action: a cohort born at the same time spreads out in reinfection count as they age, forming a coherent, advancing front. The black line in panel (e) is not a simulation—it’s an analytical prediction from Equation (5):

$$A(x)={\int }_0^x\frac{1}{\sigma (x^{\prime })}d{x}^{\prime }$$

which gives the age $A(x)$ at which a person has accumulated $x$ infections. This equation links microscopic immune dynamics to macroscopic population patterns.

What They Found

The key insight is that reinfection risk declines with infection history—and does so in a specific, quantifiable way. The researchers fit their model to two major datasets:

• Serological data on influenza A/H3N2 from Hay et al. (2013), reconstructing infection histories over a decade.
• Household incidence data for seven respiratory viruses from Monto et al. (1985), tracking symptomatic infections.

They tested different functional forms for $\sigma(x)$, the reinfection rate as a function of prior infections. A linear decline—where each infection reduces risk by a fixed amount—failed to fit the data. Instead, an exponential decay with saturation worked best:

$$\sigma (x)={\theta }_1+{\theta }_2{e}^{-{\theta }_{3}x}$$

This means reinfection risk drops rapidly at first, then levels off, approaching a baseline rate $\theta_1$ that never goes to zero. In practical terms: the first few infections provide the strongest protection; additional ones add diminishing returns.

From this, the team computed a simple but powerful metric: the number of reinfections required to halve the reinfection rate. This “halving number” varies dramatically across viruses:

Halving Number by Virus

Label	Value
RSV	0.13
HPIVs	0.16
HMPV	0.16
HCoVs	0.02
IBV	0.62
RV	1.29
IAV (H3N2)	2.79

Source: Castioni et al. (2026), inferred from age-stratified incidence data.

This chart reveals a deep biological pattern. Viruses that typically infect children—RSV, HPIVs, HMPV, HCoVs—show extremely rapid declines in reinfection risk. For RSV, just one infection cuts future risk by nearly half. For human coronaviruses, even a fraction of an infection (0.02) is enough to halve susceptibility—suggesting strong, rapid immune imprinting.

In contrast, influenza A (H3N2) declines much more slowly, with a halving number of 2.79. This means it takes nearly three infections to reduce reinfection risk by half—consistent with the observation that flu can reinfect the same person multiple times in a lifetime, even within a few years.

The model also predicts the age-dependent incidence risk ratio (IRR)—how much more likely people in a given age group are to get infected compared to the population average.

RSV Incidence Risk Ratio by Age

Label	Value
0–4	2.1
5–14	1.3
15–44	0.8
45–64	0.6
65+	0.5

Model fit to Monto et al. (1985) data; IRR >1 indicates higher-than-average infection risk.

shows the fit for several viruses.

RSV Incidence Risk Ratio by Age

Label	Value
0–4	2.1
5–14	1.3
15–44	0.8
45–64	0.6
65+	0.5

Model fit to Monto et al. (1985) data; IRR >1 indicates higher-than-average infection risk.

The model captures the steep drop in infection risk during childhood for RSV and HPIVs, and the flatter profile for influenza. Notably, for rhinovirus (RV), the halving number is 1.29—midway between childhood-focused and lifelong pathogens—consistent with the fact that both children and adults get frequent colds.

Why This Changes Things

For decades, epidemiologists have known that some viruses hit children harder, others affect all ages. But explanations have been largely qualitative: “children have weaker immunity,” or “adults have built up protection.” This model gives those intuitions a quantitative, predictive framework.

It shows that the age distribution of infections isn’t just about behavior or exposure—it’s shaped by the mathematical structure of immune memory. The faster $\sigma(x)$ declines, the more infections are front-loaded in life. This has profound implications for public health.

Consider RSV. It’s a leading cause of infant hospitalization worldwide. Vaccines are now available, but rollout strategies vary. If we know that even one infection provides strong protection, then early vaccination could mimic natural immunity and shift the entire reinfection curve. The model suggests that vaccinating infants might not just prevent immediate disease—it could reduce their lifetime infection burden, much like a natural first infection would.

Similarly, for flu, the slow decline in $\sigma(x)$ means that immunity is leakier and shorter-lived. This aligns with the need for annual vaccination. But it also suggests that vaccination strategies should account for infection history, not just age. Someone with multiple prior flu infections may respond differently to a vaccine than a flu-naive individual—even if they’re the same age.

The model also challenges a common simplification in epidemic forecasting: treating immunity as a fixed, binary state (immune or not). In reality, it’s a dynamic, cumulative process. By reducing reinfection dynamics to a traveling wave, the chain SIR model offers a way to incorporate this complexity without exploding the number of model parameters.

This is crucial for long-term planning. During the COVID-19 pandemic, disruptions to seasonal virus circulation created an “immunity debt,” leading to off-season surges in RSV and flu. Models that ignored reinfection history struggled to predict these rebounds. A framework like chain SIR could help forecast how such disruptions alter the pace of reinfection waves—and when they might resurge.

Moreover, the model’s success with two very different datasets—serological and symptomatic—suggests it captures a universal feature of immune dynamics. Whether we’re measuring antibodies or symptoms, the shape of the reinfection wave remains consistent.

What’s Next

The chain SIR model is a minimal framework, and the authors acknowledge its limitations. It assumes that infection history matters, but age itself does not—except as a proxy for how many times someone has been infected. In reality, age affects immunity in other ways: thymic output declines, comorbidities increase, and social mixing changes. Future versions could incorporate age-dependent contact rates or waning.

The model also treats all infections as equivalent. It doesn’t distinguish between mild and severe illness, or between different viral subtypes. For influenza, where immune imprinting to early strains shapes lifelong responses (Gostic et al., 2016), a more nuanced version could index immunity by strain, not just count.

And while the current model assumes constant transmission, the authors show in the supplement that seasonality and stochasticity don’t destroy the traveling wave—they just modulate it.

and

show that even with seasonal forcing or random noise, the wavefront remains predictable. This robustness makes the model promising for real-world applications.

One of the most exciting prospects is integrating this framework into public health decision-making. Right now, most vaccination policies are based on age alone. But what if we could stratify by infection history? For viruses with rapid immune buildup, like RSV, early intervention could have outsized, lifelong benefits. For others, like flu, repeated boosting may be necessary.

The halving number—0.13 for RSV, 2.79 for flu—could become a new epidemiological metric, like $R_0$, summarizing how quickly immunity accumulates. It could guide vaccine design: a successful RSV vaccine should aim to achieve what one natural infection does. For flu, we may need vaccines that mimic multiple exposures.

There are also open questions. Why do some viruses confer strong protection after one infection, while others don’t? Is it viral evolution, immune evasion, or the nature of the immune response? The model doesn’t answer this—but it gives us a language to ask the question.

In the end, this work reframes reinfection not as noise, but as signal. Every infection leaves a trace in the population’s collective immune history, and that history moves like a wave through time. By learning to read it, we may finally understand not just when epidemics happen—but why they happen to whom they do.