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Genotype networks drive oscillating endemicity and epidemic trajectories in viral evolution

This study presents an eco-evolutionary framework demonstrating that the complex topology of viral antigenic genotype networks, rather than just low-dimensional antigenic spaces, drives transitions between stable endemicity and recurrent epidemics while enabling the estimation of haplotype emergence times in real-world scenarios like H3N2 influenza.

Original authors: Santiago Lamata-Otín, Octavian C. Rotita-Ion, Alex Arenas, David Soriano-Paños, Jesús Gómez-Gardeñes

Published 2026-08-17

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CC BY 4.0

Original authors: Santiago Lamata-Otín, Octavian C. Rotita-Ion, Alex Arenas, David Soriano-Paños, Jesús Gómez-Gardeñes

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Viruses are masterful survivors, constantly reshaping themselves to slip past the defenses of the immune systems they infect. This ability, known as antigenic drift, allows pathogens like influenza to circulate in human populations for decades, causing seasonal outbreaks that never quite disappear. For a long time, scientists studying these patterns relied on simplified mental maps of how viruses change. They imagined viral evolution as a straight line or a flat grid, where a virus moves step-by-step through a limited set of options, gaining new traits one by one. While these simple models helped explain some behaviors, they failed to capture the chaotic, branching reality of how viruses actually evolve. Real-world data shows that viral mutations do not follow a single path; instead, they branch out into complex, interconnected webs where many different genetic variations can lead to the same outcome, or where a virus can jump between distant branches. Understanding the true shape of this evolutionary landscape is crucial because it determines whether a disease will settle into a steady, low-level presence or explode into recurring, seasonal epidemics.

A team of researchers has now built a new framework to explore this complexity, moving beyond simple maps to study the actual architecture of viral evolution. They focused on the influenza A virus, specifically the H3N2 strain, which is a major cause of seasonal flu. By analyzing genetic data, they reconstructed a "genotype network," a vast map where every point represents a unique genetic version of the virus, and lines connect versions that differ by just a single mutation. This map revealed a structure far more intricate than previously thought, featuring clusters of similar variants and long, winding paths that connect them. The researchers then used this real-world map to power a computer simulation of how the virus spreads through a population. In their model, they tracked how individuals get infected, how their immune systems learn to fight specific strains, and how the virus mutates as it moves from person to person. Crucially, the model remembered the history of infections for each person, allowing the simulation to account for how past exposure to one strain might offer partial protection against a related one.

When the researchers ran their simulations using the complex, real-world network of influenza genotypes, the results were striking. The virus did not settle into a calm, steady state. Instead, the intricate structure of the network itself drove the system into a cycle of recurring epidemics. The virus would surge, infecting a large portion of the population, before the immune defenses of the survivors pushed it back down, only for a new wave to emerge later as the virus found a new path through the genetic network. This oscillating behavior, which mimics the seasonal flu patterns seen in the real world, appeared simply because of the shape of the network. To prove this, the team compared their results against simulations using simplified, grid-like networks. In those flat, orderly models, the virus quickly settled into a constant, unchanging level of infection, failing to produce the dramatic peaks and valleys of a seasonal epidemic. The study suggests that the complex, branching nature of viral evolution is not just a background detail but a primary engine that drives the rhythm of disease outbreaks.

The researchers also tested whether their model could replicate the actual history of the H3N2 virus. They compared the timing of viral peaks in their simulation against the dates when specific genetic variants were first recorded in global surveillance databases. The match was remarkably close. The simulation correctly predicted when different viral lineages would rise to prominence and when they would fade away, mirroring the real-world timeline of the virus's evolution over the last several decades. This alignment gives the researchers confidence that their approach captures the essential mechanics of how the virus navigates its genetic landscape. They found that the virus often travels in "swarms" of closely related variants, which helps it overcome the immune pressure built up by the population. These swarms act as a buffer, allowing the virus to persist and eventually find a path to a new, distinct lineage that the population has not yet seen.

This work highlights that the map of viral evolution is just as important as the virus itself. The way genetic variants are connected—whether they form tight clusters, long chains, or a tangled web—dictates how the disease behaves on a population level. If the network is simple and orderly, the disease tends to become a steady, manageable presence. But when the network is complex and modular, as it is for real influenza, the system is prone to wild swings and recurring waves. The study does not claim to have solved the problem of predicting every future outbreak, but it provides a robust method for integrating real genetic data into epidemic models. By acknowledging the true, messy complexity of viral evolution, scientists can build better tools to understand why some diseases flare up seasonally while others remain constant, offering a clearer path toward anticipating the future of viral threats.

Technical Summary: Genotype Networks Drive Oscillating Endemicity and Epidemic Trajectories in Viral Evolution

Problem Statement
Rapidly evolving viruses, such as influenza and SARS-CoV-2, utilize antigenic drift to evade host immunity and establish endemicity. Traditional epidemiological models often rely on low-dimensional representations of antigenic space (e.g., one-dimensional linear chains) to study the interplay between viral evolution and epidemic spread. However, genomic surveillance data reveals that viral evolution occurs within complex, high-dimensional antigenic genotype networks characterized by hierarchical modular structures. Existing phylogenetic approaches, while valuable, often fail to capture convergent evolution and the possibility of multiple evolutionary pathways leading to the same strain. Consequently, there is a need for an eco-evolutionary framework that explicitly incorporates the complex topology of genotype networks to understand how these structures shape epidemic trajectories, specifically distinguishing between stable endemic states and recurrent seasonal epidemics.

Methodology
The authors introduce the Susceptible-Infectious-Mutation-Susceptible (SIMS) model, a compartmental framework that integrates contagion, immune dynamics, and mutation within a unified approach.

Model Structure: The population is divided into a Susceptible ( $S$ ) compartment and $n$ distinct Infectious ( $I_i$ ) compartments, where each $I_i$ corresponds to a specific viral strain $s_i$ .
Contagion: Susceptible individuals contract infections upon contact with infectious individuals at a rate $\beta$ .
Immune Response (Memory Core): Unlike standard Markovian models, the recovery rate $\mu_i(t)$ is time-dependent and stores the infection history of the population. The rate increases proportionally to the prevalence of strain $i$ and antigenically similar strains (cross-immunity), modulated by a characteristic cross-immunity length $\Delta$ . Immunity wanes over time at a rate $\gamma$ , returning to a basal recovery rate $\mu_0$ .
Mutation: Viral evolution is modeled as a diffusion process across a genotype network. Infected individuals can mutate to neighboring strains (differing by a single point mutation) at a rate $D_x$ .
Networks: The study utilizes two types of networks:
1. Synthetic Networks: Constructed to test specific topological features, including lattices (low-dimensional analogs), homogeneous concatenations of star-like clusters (mimicking mutant swarms), and heterogeneous concatenations.
2. Real-World Network: The H3N2 influenza A genotype network (based on hemagglutinin protein data), which exhibits non-trivial topological properties such as long-tailed degree distributions, high modularity, and disassortative mixing.
Analysis: The dynamics are governed by a set of coupled differential equations (mean-field approximation). The authors analyze epidemic trajectories ( $I(t)$ ) and relative prevalence ( $I_{rel}(t)$ ) across different network topologies and parameter regimes (specifically varying the immune memory timescale $\gamma$ ).

Key Contributions and Results

Topology Determines Epidemic Regimes: The study demonstrates that the topology of the genotype network alone can drive transitions between stable endemic states and recurrent seasonal epidemics.
- When the antigenic space is represented as a lattice (low-dimensional), the system converges to a steady endemic equilibrium.
- When the space is represented by complex networks with "mutant swarms" (star-like clusters), the system exhibits oscillatory, seasonal behavior.
- The size of a mutant swarm correlates with the magnitude of the corresponding outbreak peak, suggesting that the simultaneous emergence of similar genotypes helps counteract cross-immunity pressure.
Role of Immune Memory: The presence of long-lasting immune memory ( $\gamma = 0$ ) is critical for generating complex trajectories. When immune acquisition and loss timescales are compatible ( $\gamma = \alpha$ ), the macroscopic differences between network topologies diminish, and the system behaves similarly across different structures.
Real-World Reconstruction: Applying the SIMS model to the H3N2 genotype network successfully reproduces complex lineage patterns observed in public data repositories. The model captures the emergence and turnover of lineages due to antigenic fitness and clonal interference.
- The model identifies "mutant swarms" (communities) within the network that correspond to distinct peaks in the epidemic trajectory.
- There is a high correlation between the simulated peak times of strains and their actual sampling times in genomic surveillance data, indicating the model can partially reconstruct the evolutionary history of the virus.
Structural Analysis of H3N2: The analysis of the real H3N2 network reveals it possesses longer average path lengths, higher modularity, and elevated clustering coefficients compared to randomized networks with the same degree sequence. These features suggest a hierarchical organization where successful strains generate multiple antigenically similar offspring.

Significance
The paper argues that the inherent complexity of antigenic space, shaped by the vast range of potential genomic mutations, cannot be overlooked. The primary significance of this work lies in demonstrating that the topology of genotype networks is a critical determinant of epidemic behavior.

Theoretical Advancement: The study provides a robust eco-evolutionary framework that bridges the gap between real-world genomic diversity and its representation in epidemic models. It moves beyond low-dimensional embeddings to capture speciation events and convergent evolution.
Predictive Capability: By integrating real-world genotype networks, the model offers a method for estimating the emergence times of various haplotypes resulting from viral evolution.
Mechanistic Insight: The findings underscore that oscillating endemicity (seasonal waves) is not merely a result of parameter tuning but is driven by the specific structural properties of the antigenic space, particularly the interplay between infection history, cross-immunity, and the modular structure of mutant swarms.

The authors conclude that while the SIMS model provides a quantitative framework for integrating genomic data into epidemic models, full reconstruction remains challenging due to disconnected components in genotype networks. Future work may involve leveraging Bayesian inference or machine learning to reconstruct complete networks and incorporating heterogeneous contact structures and host mobility to further enhance predictive power.

Technical Summary: Genotype Networks Drive Oscillating Endemicity and Epidemic Trajectories in Viral Evolution

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