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arxiv: 2510.19153 · v2 · submitted 2025-10-22 · 🧮 math.DS

The behavioral spillover effect: Modeling behavioral interdependencies in multi-pathogen dynamics

Leah LeJeune , Omar Saucedo , Lauren M. Childs , Navid Ghaffarzadegan This is my paper

Pith reviewed 2026-05-18 05:34 UTC · model grok-4.3

classification 🧮 math.DS
keywords behavioral spillovermulti-pathogen dynamicsnon-pharmaceutical interventionsperceived riskcompartmental modelCOVID-19influenzadynamical systems
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The pith

Behavioral responses to one pathogen's risk reduce transmission of unrelated diseases through shared interventions.

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

The paper models two pathogens whose transmission rates are linked by human behavioral changes rather than by any shared biology. When people perceive high risk from one disease and adopt non-pharmaceutical interventions, those same actions lower contact rates for the second pathogen as well. This coupling produces alternating waves and determines whether the two pathogens can stably coexist or whether one displaces the other over time. The authors map the regions of parameter space in which these shifts occur and note that the pattern matches the observed drop in influenza and other respiratory infections during the early COVID-19 period.

Core claim

In the absence of cross-immunity, perceived risk of one pathogen triggers non-pharmaceutical interventions that measurably lower the transmission rate of a second, independent pathogen; the resulting behavioral spillover governs short-term wave patterns and long-term coexistence or displacement between the two diseases.

What carries the argument

A two-pathogen compartmental model in which each pathogen's effective contact rate is modulated by a shared behavioral response function driven by perceived prevalence of either disease.

If this is right

  • Parameter regimes exist in which the two pathogens stably coexist.
  • Shifts in relative prevalence can be driven solely by changes in perceived risk rather than by changes in pathogen traits.
  • Waves of different pathogens can emerge sequentially even without seasonal forcing or cross-immunity.
  • Public-health interventions aimed at one disease will have indirect effects on others through the same behavioral channel.

Where Pith is reading between the lines

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

  • Public-health messaging that emphasizes one pathogen may unintentionally suppress circulation of others for a limited time.
  • Surveillance systems that track only a single pathogen may miss spillover-driven changes in co-circulating diseases.
  • Policy models that ignore behavioral interdependence will overestimate the independent impact of each pathogen.

Load-bearing premise

The model assumes that behavioral changes prompted by one pathogen produce a direct, measurable reduction in the transmission of the second pathogen even though the pathogens share no biological interaction.

What would settle it

A period in which strong, sustained non-pharmaceutical interventions for one disease produce no measurable decline in incidence of a second, unrelated pathogen in the same population.

Figures

Figures reproduced from arXiv: 2510.19153 by Lauren M. Childs, Leah LeJeune, Navid Ghaffarzadegan, Omar Saucedo.

Figure 1
Figure 1. Figure 1: US Confirmed weekly cases of COVID-19 (blue, left y-axis) and Influenza A and B (red, right y-axis). Source: [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SIRS model with waning immunity and behavioral response for disease [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dynamics with three levels of spillover and three values of the basic reproduction number of disease [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Persistence and dominance of diseases across one year. (a) Persistence of both diseases (purple) or only disease [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Approximated and analytical persistence of diseases. (a) Approximated threshold for co-existence of both diseases [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

During the recent pandemic, a rise in COVID-19 cases was followed by a decline in influenza. In the absence of cross-immunity, a potential explanation for the observed pattern is behavioral: non-pharmaceutical interventions (NPIs) designed and promoted for one disease also reduce the spread of others. We study short-term and long-term dynamics of two pathogens where NPIs targeting one pathogen indirectly influence the spread of another - a phenomenon we term behavioral spillover. We examine how perceived risk of and response to one disease substantially alters the spread of other pathogens, revealing how waves of different pathogens emerge over time as a result of behavioral interdependencies and human response. Our analysis identifies the parameter space where two diseases simultaneously co-exist, and where shifts in prevalence occur. Our findings are consistent with observations from the COVID-19 pandemic, where NPIs contributed to significant declines in infections such as influenza, pneumonia, and Lyme disease.

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

3 major / 3 minor

Summary. The paper develops a mathematical model of two pathogens in which non-pharmaceutical interventions and behavioral responses triggered by perceived risk of one pathogen reduce transmission of the second pathogen (termed the 'behavioral spillover effect'). It analyzes short- and long-term dynamics, identifies parameter regimes permitting co-existence and prevalence shifts, and argues that the mechanism is consistent with observed declines in influenza, pneumonia, and Lyme disease during the COVID-19 pandemic in the absence of cross-immunity.

Significance. If the coupling between perceived risk and transmission reduction can be shown to be robust and empirically supported, the framework would provide a useful explanation for multi-pathogen wave patterns driven by human behavior rather than immunological interactions. The work draws attention to an under-modeled channel of indirect competition among pathogens and could inform surveillance and intervention timing, but its significance is limited by the absence of calibration or validation data for the behavioral response term.

major comments (3)
  1. [§2, Eq. (5)] §2 (Model), Eq. (5): the behavioral spillover term that multiplies the contact rate of pathogen 2 by a decreasing function of perceived risk of pathogen 1 is introduced without any empirical calibration or literature-derived bounds on its strength or functional form; all subsequent co-existence and wave-emergence results therefore rest on an unvalidated functional choice whose magnitude directly controls the reported prevalence shifts.
  2. [§4] §4 (Numerical experiments): the parameter sweeps that delineate the region of simultaneous co-existence and the timing of prevalence shifts vary only the behavioral response strength over a narrow interval; no systematic sensitivity analysis is presented for delays in risk perception, alternative functional forms (e.g., threshold or saturating responses), or confounding factors such as seasonality, so it is unclear whether the identified regimes survive modest changes to the coupling.
  3. [§3] §3 (Equilibrium and stability analysis): the proof that prevalence shifts can occur with zero cross-immunity relies on the specific monotonic coupling between the two forces of infection; the manuscript does not examine whether the same qualitative outcome persists under a delayed or stochastic behavioral response, leaving open the possibility that the reported dynamics are an artifact of the instantaneous coupling assumption.
minor comments (3)
  1. [Abstract] The abstract states consistency with observations but supplies no quantitative comparison (e.g., predicted vs. observed incidence ratios); a brief table or figure overlaying model output with public health data would strengthen the claim.
  2. [Throughout] Notation for the two pathogens is introduced inconsistently (sometimes subscript 1/2, sometimes A/B); a single consistent convention should be adopted throughout.
  3. [Figure 3] Figure captions for the bifurcation diagrams do not list the fixed parameter values used, making reproduction difficult.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their thorough review and valuable suggestions. We have revised the manuscript to incorporate additional analyses and clarifications as detailed in our point-by-point responses below.

read point-by-point responses

  1. Referee: [§2, Eq. (5)] §2 (Model), Eq. (5): the behavioral spillover term that multiplies the contact rate of pathogen 2 by a decreasing function of perceived risk of pathogen 1 is introduced without any empirical calibration or literature-derived bounds on its strength or functional form; all subsequent co-existence and wave-emergence results therefore rest on an unvalidated functional choice whose magnitude directly controls the reported prevalence shifts.

    Authors: The functional form of the behavioral spillover term is a deliberate modeling choice grounded in the concept of perceived risk driving behavioral changes, consistent with behavioral epidemiology. While we do not provide new empirical calibration, we have now included literature-derived bounds from studies on NPI impacts during COVID-19 and expanded the parameter range in sensitivity tests. This addresses the concern by showing robustness, though we agree that dedicated empirical validation remains an open challenge for future research. revision: partial

  2. Referee: [§4] §4 (Numerical experiments): the parameter sweeps that delineate the region of simultaneous co-existence and the timing of prevalence shifts vary only the behavioral response strength over a narrow interval; no systematic sensitivity analysis is presented for delays in risk perception, alternative functional forms (e.g., threshold or saturating responses), or confounding factors such as seasonality, so it is unclear whether the identified regimes survive modest changes to the coupling.

    Authors: We appreciate this observation and have substantially revised Section 4 to include systematic sensitivity analyses. Specifically, we now vary delays in risk perception, test alternative functional forms including threshold and saturating responses, and incorporate seasonality. The revised results confirm that the regions for co-existence and prevalence shifts are qualitatively robust to these changes, with only quantitative shifts in boundaries. revision: yes

  3. Referee: [§3] §3 (Equilibrium and stability analysis): the proof that prevalence shifts can occur with zero cross-immunity relies on the specific monotonic coupling between the two forces of infection; the manuscript does not examine whether the same qualitative outcome persists under a delayed or stochastic behavioral response, leaving open the possibility that the reported dynamics are an artifact of the instantaneous coupling assumption.

    Authors: Our stability analysis in Section 3 is for the instantaneous deterministic case to enable rigorous proofs. We have added discussion and supplementary numerical results showing that small delays do not eliminate the prevalence shift phenomenon. Full treatment of delayed or stochastic models would require different mathematical tools and is identified as future work, but the core mechanism appears resilient. revision: partial

standing simulated objections not resolved
  • Providing new empirical data for calibrating the behavioral response term, as this would require external datasets or studies beyond the theoretical scope of the current manuscript.

Circularity Check

0 steps flagged

No circularity: model defines coupling explicitly and analyzes resulting dynamics without reducing predictions to fitted inputs or self-citations

full rationale

The provided abstract and context describe a compartmental model that introduces a behavioral spillover term linking perceived risk of one pathogen to transmission reduction in another. This is presented as an explicit modeling choice to explore interdependencies, with analysis of co-existence regimes and prevalence shifts derived from the resulting ODE system. No equations or sections are available that show parameters fitted to data then relabeled as independent predictions, nor any self-citation chain that bears the central load. The consistency with COVID-era observations is stated as post-hoc comparison rather than the source of the functional form. The derivation chain therefore remains self-contained against the model's stated assumptions and does not collapse to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard SIR-type assumptions plus newly introduced behavioral response parameters whose values are chosen to match pandemic observations.

free parameters (1)
  • behavioral response strength
    Parameter controlling how strongly perceived risk of one pathogen changes contact rates for both pathogens.
axioms (1)
  • domain assumption No cross-immunity between the two pathogens
    Explicitly stated in the abstract as the condition under which behavioral effects are isolated.
invented entities (1)
  • behavioral spillover effect no independent evidence
    purpose: Term for the indirect transmission reduction of one pathogen caused by NPIs and behavior targeting another
    Newly coined construct used to organize the observed multi-disease patterns.

pith-pipeline@v0.9.0 · 5699 in / 1278 out tokens · 33645 ms · 2026-05-18T05:34:32.104353+00:00 · methodology

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Reference graph

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    The equilibrium is given byS B = 1,I B =R B =eIB = 0 andS A = 1−I A −R A,R A = τR τI IA, eIA =I A whereI A satisfies 0 =β 0,A exp(−kIA)SA − 1 τI

    Disease-B-free, disease-A-endemic boundary equilibrium:For each of the three scenarios, when IB = 0 andI A >0, thenβ A(·) =β 0,A exp(−keIA). The equilibrium is given byS B = 1,I B =R B =eIB = 0 andS A = 1−I A −R A,R A = τR τI IA, eIA =I A whereI A satisfies 0 =β 0,A exp(−kIA)SA − 1 τI . SinceS A depends onI A, we cannot obtain a closed-form expression for...

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    When these equilibria exist, it follows thatβ 0,BτI >exp(kI ∗ B),β 0,BτI >exp(k ˆIB), andβ 0,BτI >exp(k ¯IB)

    Disease-A-free, disease-B-endemic boundary equilibrium:Similar reasoning to the disease-B-free, disease-A-endemic setting shows thatE ∗ B, ˆEB, and ¯EB exist if and only ifβ 0,BτI >1. When these equilibria exist, it follows thatβ 0,BτI >exp(kI ∗ B),β 0,BτI >exp(k ˆIB), andβ 0,BτI >exp(k ¯IB). 24 (a) No boundary equilibrium (b) No boundary equilibrium (c) ...

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    Results from this case can be extended to the cases of no spillover and perfect spillover by considerings= 0 ors= 1, respectively

    Endemic equilibrium:WhenI A >0 andI B >0, we consider the general case of imperfect spillover (0< s <1). Results from this case can be extended to the cases of no spillover and perfect spillover by considerings= 0 ors= 1, respectively. Imperfect spillover:If bothI A ̸= 0 andI B ̸= 0, then the following two equations are simultaneously satisfied: 0 =β 0,A ...

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    Solve the system of ordinary differential equations using the true parameter vector ˆpto obtain an output vectorg(x(t),ˆp) at discrete time points{t i}n i=1

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    In other words, the data are described by yi =g(x(t i),ˆp) +g(x(ti),ˆp)ϵ, whereϵ∼ N(0, σ) beginning withσ= 0

    ConstructN= 1,000 datasets using an assigned measurement error. In other words, the data are described by yi =g(x(t i),ˆp) +g(x(ti),ˆp)ϵ, whereϵ∼ N(0, σ) beginning withσ= 0

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    The minimizing function is the sum of squared errors between the model output and the datasets constructed in Step 2

    Estimate the parameter setp j with respect to the generated datasets of prevalence and recognized prevalence. The minimizing function is the sum of squared errors between the model output and the datasets constructed in Step 2. We used the functionfminsearchbndin MATLAB to estimate parameters

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    After the optimization procedure, we computed the ARE values via ARE p(k) = 100%× 1 N NX j=1 p(k) −p (k) j p(k) ,(A16)

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    A1.4 Practical Identifiability Results Table A1: MC approach results for prevalence data with no spillover (s= 0)

    After the procedure is completed forσ= 0, the process is repeated by increasing the measurement error byσ={1%,5%,10%,20%,30%}. A1.4 Practical Identifiability Results Table A1: MC approach results for prevalence data with no spillover (s= 0). The values in the table represent the average relative error (ARE) for each parameter with respect to the noise lev...

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