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arxiv: 2511.16802 · v2 · submitted 2025-11-20 · 🧬 q-bio.PE · math.DS

A model for mosquito-borne epidemic outbreaks with information-dependent protective behaviour

Simone De Reggi , Andrea Pugliese , Mattia Sensi , Cinzia Soresina This is my paper

Pith reviewed 2026-05-17 20:04 UTC · model grok-4.3

classification 🧬 q-bio.PE math.DS
keywords mosquito-borne epidemicsprotective behaviourinformation-dependent responsebasic reproduction numbergeometric singular perturbationrecurrent epidemic waveshost compositionvector transmission
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The pith

Protective behaviour based on disease information can raise or lower the reproduction number of mosquito-borne epidemics and trigger repeated waves.

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

The paper builds a model of mosquito-borne epidemics in which humans adopt protective actions against bites when they receive information about past or current prevalence. Mosquitoes are allowed to feed on both disease-competent and non-competent hosts. The authors first show that the resulting behavioural response can either decrease or increase the basic reproduction number, depending on the strength of the response, the proportion of competent hosts, and the transmission parameters. They then assume that opinion formation occurs on a much faster timescale than infection dynamics and apply a reduction technique to obtain a simpler model of a uniform host population. Analysis of the reduced system reveals that the same behavioural mechanism can produce low-attack-rate outbreaks, speed epidemic fade-out, or instead sustain the disease through recurrent damped waves.

Core claim

The authors establish that behaviour-driven protection may either decrease or increase the basic reproduction number depending on the interaction between behavioural response, host composition, and transmission parameters. Under the assumption that opinion dynamics evolves on a much faster time scale than disease transmission, Geometric Singular Perturbation Theory reduces the original two-group model to one for a homogeneous host population; the reduced system shows that information-induced behavioural changes can facilitate epidemic control or prolong disease persistence, potentially generating recurrent damped epidemic waves and outbreaks with low attack rates.

What carries the argument

Reduction of the two-group model to a homogeneous-host model via Geometric Singular Perturbation Theory applied to fast opinion dynamics.

If this is right

  • Behaviour-driven protection may decrease or increase the basic reproduction number.
  • Protective measures can facilitate epidemic control under suitable host composition and parameters.
  • Behavioural responses may prolong disease persistence and generate recurrent damped epidemic waves.
  • Information-induced changes can produce outbreaks that reach only low attack rates.

Where Pith is reading between the lines

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

  • Public health messaging that supplies timely prevalence data might be tuned to favour the control-promoting regime rather than the persistence-promoting one.
  • The same fast-behaviour reduction could be tested on other vector-borne diseases that involve mixed host competence.
  • Collecting paired data on behavioural response speed and epidemic wave patterns would directly test whether the timescale separation holds in real populations.

Load-bearing premise

Opinion dynamics evolves on a much faster time scale than disease transmission.

What would settle it

Field or simulation data showing no recurrent damped waves and no low-attack-rate outbreaks despite strong information-dependent protective behaviour would contradict the reduced model's transient predictions.

Figures

Figures reproduced from arXiv: 2511.16802 by Andrea Pugliese, Cinzia Soresina, Mattia Sensi, Simone De Reggi.

Figure 1
Figure 1. Figure 1: The split of the human population in protected and non-protected individuals. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Flow chart for system (5). Straight lines: compartmental movements within each population; dashed lines: infections between populations (mosquitoes infecting humans and viceversa). In the following, we argue in terms of the fractions SP /H, IP /H, SNP /H, INP /H, and IM/M, which, for later convenience, will be still denoted with the same variables that have been using so far. The resulting model reads  … view at source ↗
Figure 3
Figure 3. Figure 3: The behaviour of the function F(p, q) in (15). Note that this is independent of all the parameters of the model but p and q. As for the second term on the LHS of (16), it is clear that p 1 − p + q 2p = p 1 − p(1 − q 2) < 1, for p ∈ (0, 1] and q ∈ [0, 1). Hence l hp 1 − p + q 2p − 1 i < 0, p ∈ (0, 1], q ∈ [0, 1), (18) which implies that the presence of other hosts l always contributes to reducing the value … view at source ↗
Figure 4
Figure 4. Figure 4: Rc as a function of q for different values of p and l, with ρ = 2 and epidemiological parameters as in [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: A simulation for model (5) with l = 0.25, ρ = 2, epidemiological parameters as in [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A simulation for model (5) with l = 0.25, ρ = 2, epidemiological parameters as in [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A simulation for model (5) with l = 1; ρ = 5.12, epidemiological parameters as in [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Flow chart for model (22). Then, taking into account (23), we modify (5) as follows:    S ′ P = −βH←MρIM qSP c(p, q) + l + a(J)SNP − w(J)SP , S ′ NP = −βH←MρIM SNP c(p, q) + l − a(J)SNP + w(J)SP , I ′ P = βH←MρIM qSP c(p, q) + l − γIP + a(J)INP − w(J)IP , I ′ NP = βH←MρIM SNP c(p, q) + l − γINP − a(J)INP + w(J)IP , p ′ = a(J) − [a(J) + w(J)] p, I ′ M =… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison between (24) and (45) with model parameters and initial conditions as in Section 5 with l = 0.25, ρ = 2, q = 0 (perfect protection), χ = 104 , n = 1, φ = 20 days, and from bottom to top, w0 = 0.1, 1, 10, 100 (which give Rˆ c ≈ 2.17, 1.85, 1.78, 1.77, respectively). Left: IH (defined as in (40)) as a function of time for model (24) and (45). Right: proportions SP /SH, IP /IH, p and a(J)/[a(J) + w… view at source ↗
Figure 10
Figure 10. Figure 10: Plots for (24) (red for w0 = 1, yellow for w0 = 0.1) and (45) (blue) with model parameters and initial conditions as in Section 5, l = 0.25, ρ = 2, and χ = 104 for, from top to bottom, q = 0, 0.1, 0.2, with n = 1 and φ = 30 days in (25). Left and centre: IH as a function of time. Right: RH as a function of time [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Plots for (24) (red for w0 = 1, yellow for w0 = 0.1) and (45) (blue) with model parameters and initial conditions as in Section 5, l = 0.25 and ρ = 2, and χ = 104 for, from top to bottom, q = 0, 0.1, 0.2, with n = 2 and φ = 30 days in (25). Left and centre: IH as a function of time. Right: RH as a function of time. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Plots for (24) (red for w0 = 1, yellow for w0 = 0.1) and (45) (blue) with model parameters and initial conditions as in Section 5, l = 0.25 and ρ = 2, and χ = 104 for, from top to bottom, q = 0, 0.1, 0.2, with n = 5 and φ = 30 days in (25). Left and : IH as a function of time. Right: RH as a function of time [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Plots for (24) (red for w0 = 1, yellow for w0 = 0.1) and (45) (blue) with model parameters and initial conditions as in Section 5, χ = 104 , q = 0.5, n = 1 and φ = 30 days in (25). Left: IH as a function of time. Right: RH as a function of time. The dashed lines represent the same simulations for the model without protective behaviour (q = 1). Upper row: l = 0.25 and ρ = 2. Lower row: l = 1 and ρ = 5.12. … view at source ↗
Figure 14
Figure 14. Figure 14: Plots of IH (blue) as a function of time for (45) and EE (green) as a function of SH with model parameters and initial conditions as in Section 5, l = 0.25 and ρ = 2, χ = 104 (upper row), χ = 103 (lower row), q = 0 (left) and q = 0.1 (right), with n = 1 and φ = 30 days in (25) [PITH_FULL_IMAGE:figures/full_fig_p036_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Plots of IH (blue) as a function of time for (45) and EE (green) as a function of SH with model parameters and initial conditions as in Section 5, l = 0.25 and ρ = 2, χ = 104 (upper row), χ = 103 (lower row), q = 0 (left) and q = 0.1 (right), with n = 2 and φ = 30 days in (25). 36 [PITH_FULL_IMAGE:figures/full_fig_p036_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Plots of IH (blue) as a function of time for (45) and EE (green) as a function of SH with model parameters and initial conditions as in Section 5, l = 0.25 and ρ = 2, χ = 104 (upper row), χ = 103 (lower row), q = 0 (left) and q = 0.1 (right), with n = 5 and φ = 30 days in (25) [PITH_FULL_IMAGE:figures/full_fig_p037_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Plots of IH (solid blue) as a function of time for (45), and EE (solid green) and Rˆ e (dashed black) as functions of SH, with model parameters and initial conditions as in Section 5, l = 0.25 and ρ = 2 (left), l = 1 and ρ = 5.12 (right), χ = 104 , q = 0.2, with n = 1 and φ = 30 days in (25). For each plot, the values on the vertical axis on the left (blue colour) are relevant to IH and EE, while those on… view at source ↗
read the original abstract

We investigate a model for a mosquito-borne epidemic in which human hosts may adopt protective behaviour against vector bites in response to information on both past and current disease prevalence. Assuming that mosquitoes can also feed on non-competent hosts (i.e.\ hosts that do not contribute to disease transmission), we first revisit existing results and show that behaviour-driven protection may either decrease or increase the basic reproduction number, depending on the interaction between behavioural response, host composition, and transmission parameters. Assuming that opinion dynamics evolves on a much faster time scale than disease transmission, we then apply Geometric Singular Perturbation Theory to effectively reduce the original two-group model to a model for a homogeneous host population. The reduced system enables a detailed investigation of the impact of information-induced behavioural changes on the transient dynamics of the epidemic, including scenarios in which protective measures lead to outbreaks with low attack rates. Our analysis shows that behavioural responses may either facilitate epidemic control or prolong disease persistence, potentially generating recurrent damped epidemic waves. Numerical simulations are provided to illustrate and support the analytical findings.

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 / 3 minor

Summary. The paper develops a compartmental model for mosquito-borne epidemics incorporating information-dependent protective behavior in human hosts and non-competent hosts that mosquitoes can feed upon. It revisits results on the basic reproduction number, showing that protective behavior can either decrease or increase R0 depending on behavioral response strength, host composition, and transmission parameters. Assuming fast opinion dynamics, Geometric Singular Perturbation Theory is applied to reduce the two-group model to an effective homogeneous-host model. The reduced system is then used to analyze transient dynamics, including low attack rates and the potential for recurrent damped epidemic waves, with numerical simulations provided for illustration.

Significance. If the GSPT reduction is valid with uniform attraction and the time-scale separation holds, the work offers a useful framework for examining how information-driven protective behavior modulates epidemic persistence and control in vector-borne diseases. The approach of combining behavioral response modeling with singular perturbation techniques to study transient phenomena such as damped recurrent waves is a methodological strength when the reduction is rigorously justified.

major comments (2)
  1. [GSPT model reduction] In the section applying Geometric Singular Perturbation Theory, the reduction assumes opinion dynamics evolves on a much faster time scale than disease transmission, but no explicit bounds on the separation parameter ε are derived, nor are numerical checks reported confirming that the reduced vector field reproduces key transient quantities (attack rate, damping rate of recurrent waves) for biologically plausible ε values consistent with information spread versus vector-host contact rates. This verification is load-bearing for the central claims about behavioral responses generating recurrent damped waves.
  2. [Basic reproduction number analysis] The claim that behaviour-driven protection may increase R0 (depending on host composition and transmission parameters) is stated in the abstract and introduction as a revisited result, but the manuscript provides no explicit derivation, threshold conditions, or sensitivity analysis in the relevant section to delineate the parameter regimes where the increase occurs versus a decrease.
minor comments (3)
  1. [Model formulation] The notation for the opinion dynamics variable and its coupling to the transmission rate should be introduced with a clear table of symbols in the model formulation section to improve readability.
  2. [Numerical results] Figure captions for the numerical simulations should explicitly list the default parameter values and the range of ε values tested to allow readers to assess the robustness of the illustrated wave patterns.
  3. [Discussion] A brief discussion of the biological plausibility of the assumed functional form for the protective behavior response (e.g., dependence on past vs. current prevalence) would strengthen the interpretation of the results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive report. We address each major comment below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [GSPT model reduction] In the section applying Geometric Singular Perturbation Theory, the reduction assumes opinion dynamics evolves on a much faster time scale than disease transmission, but no explicit bounds on the separation parameter ε are derived, nor are numerical checks reported confirming that the reduced vector field reproduces key transient quantities (attack rate, damping rate of recurrent waves) for biologically plausible ε values consistent with information spread versus vector-host contact rates. This verification is load-bearing for the central claims about behavioral responses generating recurrent damped waves.

    Authors: We agree that the absence of explicit bounds on ε and direct numerical validation for plausible values represents a gap that should be addressed to rigorously support the reduction. In the revised manuscript we will derive approximate bounds on ε by comparing the characteristic time scales of opinion dynamics (governed by information dissemination rates) against vector-host contact rates. We will also add a dedicated numerical subsection comparing the full two-group system and the reduced model for ε ∈ {0.01, 0.05, 0.1}, confirming that attack rates and the damping rates of recurrent waves remain quantitatively close within these ranges, which we argue are consistent with rapid social-media-driven information spread relative to slower epidemiological processes. revision: yes

  2. Referee: [Basic reproduction number analysis] The claim that behaviour-driven protection may increase R0 (depending on host composition and transmission parameters) is stated in the abstract and introduction as a revisited result, but the manuscript provides no explicit derivation, threshold conditions, or sensitivity analysis in the relevant section to delineate the parameter regimes where the increase occurs versus a decrease.

    Authors: The manuscript revisits the basic reproduction number for the two-group model with information-dependent protection in Section 3. Nevertheless, we accept that a clearer, self-contained derivation together with explicit threshold conditions and sensitivity analysis would improve readability and substantiate the claim that protection can increase R0 under certain host compositions and transmission parameters. We will expand the relevant section to include the full next-generation-matrix derivation, the resulting threshold expressions separating the regimes of R0 increase versus decrease, and a brief sensitivity analysis with respect to the behavioral response strength and the proportion of non-competent hosts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; GSPT reduction is an explicit modeling assumption applied to a new system

full rationale

The derivation begins with a standard two-group model incorporating information-dependent protective behavior and non-competent hosts. The central reduction step invokes Geometric Singular Perturbation Theory under the stated assumption that opinion dynamics evolves on a much faster timescale than disease transmission; this is presented as a methodological choice to obtain an effective homogeneous-host model rather than a quantity defined in terms of itself. Subsequent analysis of transient dynamics (attack rates, damped recurrent waves) follows directly from the reduced vector field. No fitted parameters are relabeled as predictions, no load-bearing uniqueness theorems are imported via self-citation, and no ansatz is smuggled through prior work by the same authors. The model remains self-contained against its own equations and external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The model introduces several standard epidemiological parameters (transmission rates, biting rates, recovery rates) plus new behavioral response functions and a separation-of-timescales assumption. No machine-checked proofs or external data are mentioned.

free parameters (2)
  • behavioral response strength and functional form
    The rate and shape of how protection increases with prevalence information is introduced to produce the desired non-monotonic R0 effect and wave behavior.
  • proportion of non-competent hosts
    This fraction is varied to show reversal of protection benefit and is not derived from first principles.
axioms (1)
  • domain assumption Opinion dynamics evolves on a much faster time scale than disease transmission
    Invoked to justify the geometric singular perturbation reduction; appears in the abstract as the premise for model simplification.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Kinetic models of opinion-driven epidemics on graphons prove L1 and Sobolev convergence, introduce a structure-preserving scheme, and show that a time-dependent reproduction number analog can generate waves without ex...

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