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arxiv: 2606.15578 · v1 · pith:HKID5EY7new · submitted 2026-06-14 · ⚛️ physics.soc-ph

Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring

Yusheng Li , Meiling Xie , Qin Li , Minyu Feng , Matja\v{z} Perc This is my paper

Pith reviewed 2026-06-27 04:34 UTC · model grok-4.3

classification ⚛️ physics.soc-ph
keywords adaptive epidemicshypergraphshigher-order interactionsimmunizationrewiringphase transitionsbistabilitySIS model
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The pith

Adaptive hyperedge feedback on hypergraphs induces discontinuous epidemic transitions and bistable regimes where high initial prevalence drives eradication.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an adaptive simplicial SIS model on d-uniform hypergraphs in which hyperedges representing group interactions dynamically lower their activity when local infection pressure rises. This feedback, together with risk-driven immunization and structural rewiring rules, produces discontinuous jumps between disease-free and endemic states as well as intervals of bistability. In the bistable region, sufficiently large initial outbreaks can push the entire system toward the disease-free equilibrium rather than settling at an endemic level. The analysis derives stationary-state conditions by extending a microscopic Markov-chain approximation to higher-order interactions and confirms the predictions with Monte Carlo simulations on the co-evolving node and hyperedge dynamics. Targeted immunization and degree-preferential rewiring reduce prevalence more effectively than random strategies.

Core claim

In the adaptive s-SIS model on d-uniform hypergraphs, hyperedge activity decreases in response to local infection pressure, inducing discontinuous phase transitions, nonlinear epidemic thresholds, and bistable regimes in which sufficiently high initial prevalence drives the system to the disease-free equilibrium. Risk-driven immunization, combining spontaneous isolation with targeted deactivation, and structural rewiring, either random or degree-preferential, are introduced as hyperedge-level interventions. Extending the microscopic Markov chain approximation yields analytical conditions for the existence and stability of endemic and disease-free states, while simulations confirm that target

What carries the argument

adaptive hyperedge feedback in the s-SIS model on d-uniform hypergraphs, where hyperedge activity co-evolves with node states according to local infection pressure and intervention rules.

If this is right

  • Adaptive hyperedge feedback produces discontinuous phase transitions between disease-free and endemic states.
  • Bistable regimes appear in which high enough initial prevalence drives the system to the disease-free equilibrium.
  • Epidemic thresholds become nonlinear functions of transmission parameters because of the co-evolution between nodes and hyperedges.
  • Targeted immunization and degree-preferential rewiring suppress steady-state prevalence more than random counterparts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Group-level self-isolation policies keyed to internal infection counts could create self-correcting outbreak dynamics in real clustered populations.
  • The bistability suggests that temporary surges in reported cases might sometimes resolve without further intervention if feedback thresholds are met.
  • Similar adaptive mechanisms might be tested on non-uniform hypergraphs to check whether the discontinuous and bistable features persist beyond fixed group size.

Load-bearing premise

The microscopic Markov chain approximation can be extended to accurately capture higher-order interactions and the co-evolution of node states with hyperedge activity on d-uniform hypergraphs.

What would settle it

Monte Carlo runs on the same d-uniform hypergraphs that fail to exhibit discontinuous jumps or bistability when initial prevalence is varied would falsify the claimed induction of those regimes by adaptive hyperedge feedback.

Figures

Figures reproduced from arXiv: 2606.15578 by Matja\v{z} Perc, Meiling Xie, Minyu Feng, Qin Li, Yusheng Li.

Figure 1
Figure 1. Figure 1: Schematic illustration of the adaptive epidemic model on uniform hy￾pergraphs. (a) Demonstration of the s-SIS model. Red and blue circles represent infected and susceptible nodes, respectively, connected by hyperedges (light blue regions). Infection spreads with rate βd when all d − 1 other members in a hyperedge are infected, whereas each infected node recovers independently at rate µ. (b) Illustration of… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between theoretical predictions from MMCA equations and MC simulations on adaptive hypergraphs. Panel (a) shows the infection density ρ I in the stationary state as a function of infection rate β under different average hyperdegrees ⟨k⟩ = 6, 9, 12. Panels (b) and (c) display the temporal evolution of susceptible (S) and infected (I) fractions ρ for ⟨k⟩ = 12 at β = 0.08 and β = 0.10, respectively… view at source ↗
Figure 3
Figure 3. Figure 3: The effects of initial conditions and adaptive parameters on outbreak dynamics and stationary-state prevalence. Time evolution of the infection density ρ I (t) over 103 time steps under different initial conditions I(0), shown for (a) varying sensitivity η and (d) varying spontaneous recovery rate γ. Panels (b) and (c) give the stationary-state infection density ρ I as a function of β and η for I(0) = 0.2 … view at source ↗
Figure 4
Figure 4. Figure 4: Comparative effectiveness of immunization strategies. Performance com￾parison among Targeted immunization (TI), Random edge immunization (Random), and Spontaneous isolation (SI) strategies under varying activity thresholds θmin = 0.2, 0.4, 0.6 for SI1, SI2, and SI3, respectively. Panels (a)–(d) correspond to four parameter settings: (a) ⟨k⟩ = 6, γ = 0.02; (b) ⟨k⟩ = 9, γ = 0.02; (c) ⟨k⟩ = 6, γ = 0.03; and (… view at source ↗
Figure 5
Figure 5. Figure 5: Herd immunity threshold wc under different immunization strategies. The critical immunization fraction wc, defined as the minimum proportion of immunized hyperedges required to eliminate epidemics, is shown as a function of the infection rate β for two initial infection levels: (a) I(0) = 0.3 and (b) I(0) = 0.5. Results are compared across Targeted immunization (TI), three variants of Spontaneous isolation… view at source ↗
Figure 6
Figure 6. Figure 6: Impact of rewiring mechanisms on epidemic dynamics and network topology. Panels (a) and (c) show the time evolution of infection density under random rewiring and degree-preferential rewiring, respectively, following targeted immunization ap￾plied at the intervention moment. Panels (b) and (d) compare the degree distributions P(k) before and after random rewiring and degree-preferential rewiring. At time t… view at source ↗
Figure 7
Figure 7. Figure 7: Performance of the proposed model and intervention strategies on the congressional bill cosponsorship hypergraph: (a) Stationary infection density ρ I as a function of the infection rate β under different sensitivity parameters η. (b) Compari￾son of different immunization strategies among targeted immunization (TI), random edge immunization (Random), and spontaneous isolation with threshold θmin = 0.2 (SI1… view at source ↗
read the original abstract

Understanding how higher-order social structures shape epidemic spreading requires models that couple group interactions with adaptive behavior. We introduce an adaptive simplicial susceptible-infected-susceptible (s-SIS) model on d-uniform hypergraphs, where both node states and hyperedge activity co-evolve in response to local infection pressure. Hyperedges represent group interactions of fixed size and dynamically reduce their activity through a feedback mechanism in highly infected environments. Within this framework, we design two classes of hyperedge-level interventions: (i) risk-driven immunization, combining spontaneous, activity-based isolation with targeted deactivation guided by hyperedge infection pressure, and (ii) structural rewiring, which reconstructs group structures either randomly or via degree-preferential attachment. By extending the microscopic Markov chain approximation to higher-order interactions, we derive analytical conditions for the existence and stability of both endemic and disease-free stationary states. Our analysis shows that adaptive hyperedge feedback can induce discontinuous phase transitions, nonlinear epidemic thresholds, and bistable regimes in which sufficiently high initial prevalence drives the system to a disease-free equilibrium. Extensive Monte Carlo simulations support the theory and confirm that targeted immunization and degree-preferential rewiring substantially suppress epidemic prevalence, outperforming random strategies. These results demonstrate that higher-order interactions and adaptive group-level responses fundamentally reshape epidemic bifurcations and suggest principles for designing effective intervention policies in complex social systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces an adaptive s-SIS epidemic model on d-uniform hypergraphs in which node states and hyperedge activity co-evolve via infection-pressure feedback. Two intervention classes are defined: risk-driven immunization (spontaneous plus targeted deactivation) and structural rewiring (random or degree-preferential). An extension of the microscopic Markov chain approximation (MMCA) to higher-order interactions yields analytical conditions for the existence and stability of endemic and disease-free equilibria. The analysis predicts that adaptive hyperedge feedback produces discontinuous phase transitions, nonlinear thresholds, and bistable regimes in which high initial prevalence can drive the system to the disease-free state. Monte Carlo simulations are reported to support the theory and to show that targeted immunization and degree-preferential rewiring outperform random strategies in suppressing prevalence.

Significance. If the MMCA closure remains accurate under adaptive hyperedge dynamics, the work supplies a concrete mechanism by which group-level adaptation reshapes epidemic bifurcations and supplies testable intervention principles. The explicit derivation of stationary-state conditions together with direct simulation comparisons constitutes a strength; the absence of free parameters in the core model rules is also noted.

major comments (2)
  1. [Derivation of stationary-state conditions (MMCA extension)] The central claims of discontinuous transitions, nonlinear thresholds, and bistability rest on the stationary-state conditions obtained from the MMCA extension to d-uniform hypergraphs with adaptive hyperedge activity (abstract and the section deriving the stationary-state equations). This closure necessarily omits dynamical correlations between node states and the rewiring/immunization rules; on hypergraphs such correlations are expected to be stronger than in pairwise networks, especially under degree-preferential rewiring. If the neglected terms alter the bifurcation diagram, the reported qualitative phenomena could be artifacts of the approximation rather than properties of the underlying stochastic process. A direct comparison of the MMCA predictions against exact stochastic realizations on small hypergraphs, or an explicit error bound, is required to establish that the claimed regi
  2. [Monte Carlo simulation results section] Table or figure reporting the Monte Carlo validation of the bistable regime (high initial prevalence driving the system to disease-free equilibrium) should include the precise initial-condition sampling protocol and the number of independent runs per parameter point; without these details it is impossible to assess whether the observed bistability is robust to stochastic fluctuations that the MMCA neglects.
minor comments (2)
  1. [Model definition] Notation for the hyperedge activity variable and its feedback function should be introduced with an explicit equation number at first use to avoid ambiguity when the same symbols appear in both the immunization and rewiring sections.
  2. [Figure captions] The abstract states that 'extensive Monte Carlo simulations support the theory'; the corresponding figure captions should state the hypergraph size, the range of d values tested, and whether the same random seeds were used for the adaptive and non-adaptive cases.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating where revisions will be made.

read point-by-point responses

  1. Referee: The central claims of discontinuous transitions, nonlinear thresholds, and bistability rest on the stationary-state conditions obtained from the MMCA extension to d-uniform hypergraphs with adaptive hyperedge activity (abstract and the section deriving the stationary-state equations). This closure necessarily omits dynamical correlations between node states and the rewiring/immunization rules; on hypergraphs such correlations are expected to be stronger than in pairwise networks, especially under degree-preferential rewiring. If the neglected terms alter the bifurcation diagram, the reported qualitative phenomena could be artifacts of the approximation rather than properties of the underlying stochastic process. A direct comparison of the MMCA predictions against exact stochastic realizations on small hypergraphs, or an explicit error bound, is required to establish that the claimed regi

    Authors: We acknowledge that the MMCA constitutes a closure approximation that neglects dynamical correlations, which can indeed be stronger under adaptive hyperedge rules on hypergraphs. The manuscript validates the MMCA predictions through direct Monte Carlo simulations on finite hypergraphs of varying sizes, demonstrating quantitative agreement in threshold locations, transition types, and bistable regimes. This cross-validation across system sizes indicates that the qualitative phenomena are robust features of the model rather than pure artifacts. We will add an explicit discussion of the approximation's limitations and the supporting simulation evidence in the revised text, but a full exact enumeration on small instances for all regimes would require new computational work. Hence partial revision. revision: partial

  2. Referee: Table or figure reporting the Monte Carlo validation of the bistable regime (high initial prevalence driving the system to disease-free equilibrium) should include the precise initial-condition sampling protocol and the number of independent runs per parameter point; without these details it is impossible to assess whether the observed bistability is robust to stochastic fluctuations that the MMCA neglects.

    Authors: We agree that these methodological details are essential for assessing robustness to stochasticity. In the revised manuscript we will augment the Monte Carlo section and relevant figure captions with the exact initial-condition protocol (uniform random selection of an initial infected fraction) and the number of independent realizations per parameter point used for averaging. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in model rules and external validation

full rationale

The paper extends the microscopic Markov chain approximation (MMCA) to derive stationary-state conditions for the adaptive s-SIS model on d-uniform hypergraphs. This is a standard closure applied to the stated transition probabilities for node states and hyperedge activity, not a self-definition or fitted-input renaming. Results are cross-checked against independent Monte Carlo simulations, and no load-bearing self-citations or uniqueness theorems from prior author work are invoked to force the outcomes. The discontinuous transitions and bistability arise from the adaptive feedback and intervention rules rather than reducing to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the Markov chain approximation extends to hypergraphs and on the specific functional form chosen for hyperedge activity reduction; no free parameters or invented entities are explicitly listed in the abstract.

axioms (1)
  • domain assumption The microscopic Markov chain approximation extends to higher-order interactions on d-uniform hypergraphs
    Invoked to derive existence and stability conditions for endemic and disease-free states.

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