{"id":"79b18581-e111-42a0-a79e-20f70045664d","arxiv_id":"2602.05915","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"On hypergraph SIS models, awareness strategies based on absolute, higher-order information reduce epidemic prevalence more and impose lower social cost than pairwise or relative strategies, by concentrating alert on hubs and large groups.","lead":"A simulation and mean-field study of epidemic spread on hypergraphs finds that adaptive behaviors triggered by group-level or absolute information (e.g., counting infected groups) beat pairwise or relative-information strategies at both limiting the outbreak and keeping the 'social cost' of behavior change low. The reason is that these strategies concentrate alertness on high-contact individuals and large groups, defusing the superspreading that otherwise sustains the epidemi","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Absolute-strategy normalization by population means (Eqs. 2, 4, 6) is an uncalibrated modeling choice; the headline efficacy/cost hierarchy may flip under alternative normalizations.","rationale":"The paper is a careful modeling study with a closed IBMF, good simulation/mean-field agreement, and extensive tests across datasets and synthetic hypergraphs. The θ-dependence noted by the reader is already acknowledged in Sec. IV.B.4, where the authors state that for θ > 2/3 the higher-order strategies become less efficient—so that overclaim is explicit but qualified in the text. The more fundamental, unaddressed soft spot is the normalization of absolute strategies. The comparison between absolute and relative information is the backbone of the absolute-vs-relative and higher-order-vs-pairwise conclusions, and the 'lower social cost' result is particularly sensitive to the global scale of f_abs. Since the mean normalization is introduced without a robustness check or a derived principle that uniquely fixes it, the headline hierarchy could change under equally plausible normalizations. This is not a fatal flaw—the mechanism of hub-focused heterogeneous awareness is plausible and supported by the simulations—but it warrants a conditional verdict until the calibration is stress-tested. I therefore agree with the reader's weakest_assumption and keep the CONDITIONAL verdict.","tokens_in":37267,"tokens_out":5269,"duration_ms":60672,"concrete_test":"Re-run the pairwise and higher-order simulations on the hospital (LH10) hypergraph at r = 0.05, θ = 0.3, with absolute-strategy awareness functions multiplied by c ∈ {0.1, 0.3, 1, 3, 10} (i.e., normalize by c<k>, c<s>, c<D> in Eqs. 2, 4, 6). For each c, record I∞ and <λ∞>/λ0 for all six strategies. If the ordering ng,nw > nn > fg > fw > fn and the lower-cost ordering of ng/nw persist across all c, the normalization concern is resolved. If any c reverses the ordering or moves ng/nw to high-cost regimes, the headline claim must be restricted to the chosen mean normalization.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central comparison between absolute and relative strategies—and hence the headline claim that higher-order absolute information outperforms pairwise relative information—depends on an arbitrary calibration. In Eqs. (2), (4), and (6), the absolute awareness functions f_nn, f_nw, and f_ng are divided by the network-level means <k>, <s>, and <D>, while relative strategies normalize by node-specific totals. This choice sets the overall scale of the absolute strategies' awareness: because λ_i = λ0 exp(-f_i), multiplying f_abs by a constant c (equivalently, normalizing by c<k>, c<s>, c<D>) changes every absolute-strategy node's transmission parameter. A small c makes absolute strategies extremely cautious, potentially reducing prevalence at the price of high social cost; a large c makes them nearly inactive, eroding their apparent advantage. The paper's \"lower social cost\" claim for ng and nw is derived from the average <λ∞>/λ0 being close to 1 while prevalence is low; that balance is directly tied to the chosen normalization. No robustness analysis is provided, so the hierarchy ng,nw > nn > fg > fw > fn and the cost ordering may be artifacts of this specific calibration rather than robust properties of the mechanisms.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies SIS contagion on empirical and synthetic hypergraphs, comparing six adaptive strategies in which node transmission parameters λ_i(t) = λ_0 exp(-f_i(t)) are reduced according to an awareness function f_i based on pairwise, hybrid, or higher-order (group) information, each in either absolute or relative form. The central claim is that strategies based on absolute higher-order information (ng and nw) are the most effective at reducing epidemic prevalence and also have the lowest social cost, because they concentrate risk perception on high-hyperdegree nodes and large groups, effectively acting as a targeted immunization mechanism. The paper supports this with 300-run agent-based simulations, an individual-based mean-field (IBMF) approach, and results across six empirical datasets and several synthetic hypergraphs.","tokens_in":37563,"tokens_out":3091,"duration_ms":38516,"significance":"If the central hierarchy is robust, the paper provides a useful design principle for adaptive behavioral interventions in settings with group interactions: using absolute higher-order information can yield both better epidemic control and lower social cost than relative or pairwise-only strategies. The systematic comparison across multiple strategies, the closed IBMF equations, and the analysis of microscopic mechanisms (first-infection times, hyperdegree-dependent awareness) are valuable contributions. The paper does not fit parameters to data, and the simulations and mean-field agree well, which strengthens the internal validity of the reported phenomenology.","major_comments":[{"comment":"The abstract and introduction claim without qualification that 'adaptive behaviors driven by higher-order information are more effective ... than similar mechanisms based on pairwise information.' However, Fig. 7a and the accompanying text state that for θ > 2/3, the higher-order strategies ng and fg are less efficient than the other strategies. This is a direct overstatement of the results. The abstract and conclusions should be qualified to state the range of θ (and possibly the dataset-specific range) for which the hierarchy holds; otherwise the central claim is stronger than the evidence.","section":"Section IV B 4, Fig. 7"},{"comment":"The absolute awareness functions are normalized by the population means ⟨k⟩, ⟨s⟩, and ⟨D⟩. This calibration sets the overall scale of the absolute strategies relative to the relative strategies, and the headline comparisons (e.g., ng vs fn, and the 'lower social cost' of ng/nw) depend on this choice. The manuscript states only that this is done 'to make mechanisms ... comparable,' but does not justify why the mean is the appropriate scale nor test sensitivity to alternative normalizations (e.g., median, maximum, or a constant factor). Since a rescaling of the absolute f_i changes every λ_i(t) exponentially, the efficacy/cost hierarchy could flip under another natural normalization. Please provide a robustness analysis or a principled argument for the chosen calibration; otherwise the main claim must be restricted to this specific modeling choice.","section":"Eqs. (2), (4), (6) and Section II B"},{"comment":"The IBMF derivation for the hybrid strategies (fw and nw) uses the approximation W_i(n,t) ≈ n ⟨w⟩_I(t), which replaces the exact sum over infected-neighbor configurations by the mean weight of infected neighbors. This is an uncontrolled approximation in what is otherwise presented as a closed analytic derivation. While the simulation–mean-field agreement is good for the parameter values shown, the validity of this approximation for other parameter regimes and for the strategy hierarchy should be discussed. Please at least explicitly state that this is an approximation and, ideally, assess its error against the exact combinatorial expression for small-degree nodes.","section":"Section VI D, Eqs. (20)-(23)"}],"minor_comments":[{"comment":"The sentence 'a clear hierarchy is observed ... which does not depend on the epidemic parameter r' is based on a finite range of r and on specific datasets; the SM shows analogous results but not a systematic scan over r for all datasets. Please soften to 'in the parameter range explored.'","section":"Abstract / Section IV A"},{"comment":"In the definition of the ng/fg strategies, the threshold θ uses the condition i_e > θ(|e|-1). This is clear, but the notation 1_θ(e,i) is introduced before its definition in the same paragraph. Move the definition of the indicator function to just before Eq. (6).","section":"Section II B, Eqs. (2)-(7)"},{"comment":"The term 'asymptotic state' is used both for the absorbing state and for the endemic steady state. In the Methods, 'asymptotic state' for the integration of mean-field equations refers to Pi(t→∞) while for simulations T is finite. Consider using 'quasi-stationary state' for the finite-time simulation average to avoid ambiguity.","section":"Section VI C"},{"comment":"The figure captions for synthetic hypergraphs say 'Analogous to Supplementary Fig. 2/3/4...' but do not restate the definition of the r values for each panel. While acceptable for an SM, it would help readability to list the r values in each caption.","section":"Supplementary Material, Fig. 15-19"}],"recommendation":"major_revision","confidential_remarks":"The paper is technically sound in its core: the simulations are extensive, the IBMF is a closed set of ODEs for most strategies, and the empirical/synthetic hypergraph coverage is broad. The main issues are the unqualified abstract claim (contradicted by the paper's own θ>2/3 result) and the absent robustness analysis for the absolute/relative normalization, which is load-bearing for the headline comparison. These are fixable with additional analysis and a more careful statement of scope; I do not see a fundamental error that would require rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe useful core of this paper is a clean, systematic model study: six awareness strategies on pairwise and higher-order SIS contagion, compared across six empirical hypergraphs and several synthetic ones, with a closed individual-based mean-field that tracks the simulations well. The main new result is the hierarchy—absolute higher-order information (ng, nw) beats relative pairwise (fn, fw) on both prevalence and the social-cost proxy—and the mechanism the authors identify, heterogeneous risk perception concentrated on high-hyperdegree nodes and large groups, is plausible and supported by the correlation analyses. This is genuinely new relative to the companion paper, which only treats nn and ng near the transition. The math is sound: the IBMF is closed and the threshold invariance is re-derived.\n\nThe soft spots are in the framing. The stress-test note is right: the absolute strategies are normalized by population means (⟨k⟩, ⟨s⟩, ⟨D⟩), and that scale sets the trade-off. Multiply f_abs by a constant and you can make absolute strategies either almost inactive or extremely costly; the hierarchy and the 'lower social cost' conclusion are not scale-invariant. The authors present the mean normalization as a way to make the mechanisms comparable, but that is a modeling choice, not a consequence of the model, and no robustness test is offered. The abstract should not state the ranking as a general fact without this qualification. Also, the abstract omits that the higher-order strategies lose their edge for θ > 2/3; the main text discloses this, but the catchline overreaches. Minor issues: no code, and Fig. 7 markers have no error bars. None of these are fatal, and the paper is more careful than most in checking multiple structures and both contagion types.\n\nWho gets value: anyone modeling behavioral-epidemic coupling on hypergraphs. It would receive a serious referee: the comparison framework is useful, the derivations are reproducible, and the mechanism is worth investigating further, even if the headline needs a caveat.\n\nRecommendation: accept for review, and put the calibration robustness and the θ-qualification on the revision list.","headline":"A clean and useful model comparison whose headline ranking rests on an unexamined normalization choice and an understated θ-dependence.","tokens_in":38046,"tokens_out":2725,"would_cite":true,"duration_ms":30940,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Adaptive behaviors that track group-level risk contain epidemics more effectively and at lower social cost than pairwise information-based strategies.","keywords":["contagion dynamics","hypergraphs","adaptive behavior","risk perception","higher-order interactions","epidemic mitigation","social cost","mean-field approach"],"falsifier":"Run the same six-strategy comparison on a given hypergraph but normalize the absolute strategies by the median—or by each node's own baseline—of degree, strength, and hyperdegree. If ng and nw no longer dominate nn, fg, fw, and fn in both prevalence reduction and social cost, the paper's central conclusion fails for that calibration. A second test: check whether the hierarchy persists when the 'infectious group' threshold θ is set by a per-node adaptive rule rather than a fixed fraction.","tokens_in":37099,"feed_emoji":"🦠","tokens_out":4370,"duration_ms":50080,"temperature":0.7,"pith_summary":"This paper asks which kind of local awareness best helps a population curb a spreading contagion: awareness based on one-on-one contacts or awareness based on the groups a person belongs to. Modeling both pairwise and group (higher-order) contagion on hypergraphs, it compares six adaptive strategies that reduce an individual's contagion risk in response to perceived danger. The central finding is that strategies using absolute counts of 'infectious groups'—groups containing a sufficiently large fraction of infected members—outperform strategies based on pairwise information, both in reducing final epidemic prevalence and in lowering the social cost, measured as the average reduction of interaction intensity. The mechanism is a heterogeneous alert pattern: the best strategies concentrate strong caution on high-hyperdegree nodes and large groups, the very nodes and groups that otherwise drive and sustain the spread. This hierarchy is robust across pairwise and higher-order contagion processes and across several empirical and synthetic hypergraphs.","feed_headline":"Group-level alerts beat pairwise caution at lower cost","feed_subtitle":"Counting risky groups, not just contacts, contains epidemics best and preserves more social activity.","key_machinery":"The central object is the awareness function f_i(t) that exponentially reduces a node's transmission parameter, λ_i(t) = λ_0 e^{-f_i(t)}, encoding self-protection and altruism. Six strategies define f_i from different information: absolute (number) versus relative (fraction) counts of risky interactions, and pairwise, hybrid (weighted), or higher-order (group) sources. The decisive mechanism is the self-reinforcing heterogeneity produced by absolute higher-order strategies: hubs and large groups perceive many infectious events, lower their λ more strongly, and consequently become less susceptible and less infectious, so the spread decouples from the structures that normally sustain it. An in","core_discovery":"On its own terms, the paper establishes that, among six local awareness strategies that weaken transmission when risk is perceived, the two grounded in absolute higher-order information—counting how many of a node's groups are 'infectious' (ng) and the weighted count of contacts with infectious individuals (nw)—are the most effective at reducing epidemic prevalence and are also the least costly in terms of average behavioral change. Relative strategies (fractions of infectious neighbors, weights, or groups) and pairwise strategies yield larger reductions in overall activity but smaller reductions in prevalence. The authors attribute this advantage to heterogeneous risk perception: absolute h","pith_inferences":["The paper's cost metric averages behavioral change over all individuals; the best strategies actually concentrate the burden on hubs. Whether that uneven distribution is socially acceptable is a policy question the model does not address.","The absolute-versus-relative comparison hinges on normalizing absolute counts by the population mean (degree, strength, hyperdegree); normalizing by the median or by each node's own baseline could shrink or alter the reported hierarchy, so the ranking should be read as conditional on that calibration.","A testable extension: in temporal hypergraphs or when groups merge and split, the advantage of ng/nw may persist or vanish depending on how group identity evolves; the paper does not test that regime.","The mechanism suggests a possible information-campaign design principle: telling people how many risky group exposures they have, rather than what fraction of their contacts are risky, may protect the population while preserving more normal social activity."],"forward_implications":["If correct, simple local heuristics that focus on group gatherings rather than one-on-one contact counts could provide both stronger epidemic mitigation and less overall social disruption.","Targeted-like protection can emerge endogenously, without any central coordination or global topological knowledge, simply by making people aware of how many of their groups are 'infected.'","The same strategy hierarchy applies to both pairwise and nonlinear higher-order contagion processes, and adaptive behaviors can tame the explosive, bistable transitions typical of higher-order contagion.","The paper's two-dimensional comparison—efficacy in reducing prevalence and social cost as activity reduction—provides a general framework for assessing future adaptive behavioral mechanisms.","The differences between strategies amplify with hyperdegree heterogeneity and hyperedge overlap, and vanish when the underlying hypergraph is homogeneous or pairwise, clarifying when higher-order awareness matters."],"fun_headline_variants":["Group-based awareness outperforms pairwise at lower cost","Counting groups curbs contagion better than contacts","Higher-order info: containment with less social sacrifice","Group signals best for epidemics, least restrictive","Adaptive behavior via groups beats pairwise strategies"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"To compare absolute-count and fraction-based strategies on equal footing, the paper normalizes absolute counts by the population mean (mean degree, mean strength, mean hyperdegree); if a different reference were used, the reported hierarchy of efficacy and social cost could change.","fun_headline_variants_meta":{"raw":{"variants":["Group-based awareness outperforms pairwise at lower cost","Counting groups curbs contagion better than contacts","Higher-order info: containment with less social sacrifice","Group signals best for epidemics, least restrictive","Adaptive behavior via groups beats pairwise strategies"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000199,"raw_usage":{"total_tokens":1204,"prompt_tokens":735,"completion_tokens":469,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":479,"completion_tokens_details":{"reasoning_tokens":400}},"tokens_in":479,"tokens_out":469,"duration_ms":5573,"temperature":1.0,"reasoning_tokens":400,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T04:03:24.669168+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same six-strategy comparison on a given hypergraph but normalize the absolute strategies by the median—or by each node's own baseline—of degree, strength, and hyperdegree. If ng and nw no longer dominate nn, fg, fw, and fn in both prevalence reduction and social cost, the paper's central conclusion fails for that calibration. A second test: check whether the hierarchy persists when the 'infectious group' threshold θ is set by a per-node adaptive rule rather than a fixed fraction.","supporting_citations":[],"review_version":1}