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arxiv: 2606.31768 · v1 · pith:VU6X5BHVnew · submitted 2026-06-30 · 🧬 q-bio.PE · math.DS

Nonlinear Feedbacks Between Host Behavior and Vector Adaptation in a Multi-Host Vector-Borne Disease Model

Shravani Shetgaonkar , Anupama Sharma This is my paper

Pith reviewed 2026-07-01 02:13 UTC · model grok-4.3

classification 🧬 q-bio.PE math.DS
keywords vector-borne diseasemulti-host modelITN adoptionnonlinear dynamicsbifurcation analysishost behaviorvector adaptationpayoff-based decisions
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The pith

Complete ITN adoption by the primary host can increase disease prevalence in the secondary host through vector feeding shifts.

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

The paper constructs a multi-host model in which hosts decide whether to adopt insecticide-treated nets according to a payoff comparison of cost against infection risk. Vector feeding preference is allowed to vary with the resulting ITN coverage, producing a nonlinear feedback between behavior and transmission. Analysis of the resulting system shows that this coupling can drive the counterintuitive outcome in which 100 percent adoption by one host raises overall prevalence in the other. The same mechanism also permits saddle-node and Hopf bifurcations that separate stable endemic states from sustained oscillations. These results indicate that behavioral responses must be treated as endogenous when evaluating interventions in multi-host settings.

Core claim

In the model, the nonlinear coupling between payoff-driven ITN adoption and coverage-dependent vector preference creates thresholds R0 and Rc that govern the existence and stability of disease-free and endemic equilibria. Under this coupling the system can exhibit saddle-node and Hopf bifurcations, and complete ITN adoption by the primary host can increase overall prevalence in the secondary host because vectors redirect bites toward the unprotected host.

What carries the argument

The nonlinear coupling between payoff-based host ITN adoption and vector preference expressed as a function of ITN coverage.

If this is right

  • The interaction of perceived ITN cost and infection risk can trigger regime shifts from stable endemic equilibria to periodic oscillations.
  • Saddle-node bifurcations allow multiple stable prevalence levels for the same parameter values.
  • Hopf bifurcations occur when the perceived cost of ITN lies in an intermediate range relative to infection risk.
  • The counterintuitive prevalence increase in the secondary host is a direct consequence of the adaptive vector shift once primary-host coverage exceeds a critical threshold.

Where Pith is reading between the lines

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

  • Intervention planning in multi-host systems must weigh cross-species effects rather than optimizing coverage for a single host alone.
  • Similar behavioral feedbacks may arise in other zoonotic or multi-species transmission settings where one host's protective behavior alters vector contact rates with others.
  • Field studies could test the model by tracking vector host-choice indices as ITN coverage varies across co-occurring host populations.

Load-bearing premise

Vector preference changes with ITN coverage so that bites are redirected to the secondary host when the primary host adopts nets at high levels.

What would settle it

A measured rise in secondary-host prevalence after primary-host ITN coverage reaches 100 percent, while holding other transmission parameters fixed.

read the original abstract

Insecticide-treated nets (ITN) are an effective and low-cost intervention for controlling vector-borne disease (VBD), however, their use depends on individual decisions based on perceived cost and risk of infection. This study investigates a nonlinear multi-host model for the transmission of VBD with endogenous strategic control. We assume that hosts' adoption of ITN emerges from the payoff-based decision-making, creating a nonlinear coupling with disease prevalence. We model vector preference as a function of ITN coverage to probe the complex interplay among individual choices, disease prevalence, and its control in a multi-host setting. The qualitative behavior of the system is characterized by the thresholds $R_0$ and $R_c$, which determine the existence and local stability of the disease-free and endemic equilibria. The system exhibits rich dynamical behavior; hence, we provide a bifurcation analysis identifying the conditions for saddle-node and Hopf bifurcations. Our results demonstrate that the interaction between the perceived cost of ITN and the infection risk can induce critical transitions, including regime shift from stable endemic states to sustained periodic oscillations. Furthermore, we identify a counterintuitive effect whereby complete ITN adoption by the primary host can increase the overall prevalence in the secondary host due to adaptive shifts of vector feeding behavior.

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 / 0 minor

Summary. The manuscript develops a nonlinear multi-host model for vector-borne disease transmission in which host ITN adoption arises endogenously from payoff-based decision making and vector feeding preference is an (unspecified) function of ITN coverage. Equilibria are characterized by the thresholds R0 and Rc; bifurcation analysis identifies conditions for saddle-node and Hopf bifurcations. The central result is that complete ITN adoption by the primary host can increase overall prevalence in the secondary host through adaptive vector feeding shifts.

Significance. If the reported counterintuitive prevalence effect is robust, the work would usefully illustrate how behavioral feedbacks and multi-host dynamics can produce non-monotonic intervention outcomes. The bifurcation analysis also contributes to understanding possible regime shifts between endemic equilibria and periodic oscillations. However, because the effect traces directly to the choice of the two unspecified nonlinear functions, the result remains conditional on functional forms that are not shown to be generic or empirically grounded.

major comments (2)
  1. [Abstract / Model section] Abstract and model formulation: the vector preference is stated to be 'a function of ITN coverage' and host adoption is 'payoff-based,' yet no explicit functional expressions, payoff matrix, or decision dynamics are supplied. Because the direction of the secondary-host prevalence increase, the location of Rc, and the occurrence of the reported bifurcations all depend on these choices, the central claim cannot be assessed for robustness without the precise ODE system.
  2. [Bifurcation analysis] Bifurcation analysis: the conditions for saddle-node and Hopf bifurcations are asserted to arise from the nonlinear coupling, but without the explicit forms of the preference and payoff functions it is impossible to verify whether these bifurcations are structural or artifacts of particular parameterizations of the free functions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments highlighting the need for explicit model details. We agree that the current presentation leaves the functional forms implicit, which limits assessment of robustness. We will revise the manuscript to include the precise ODE system, payoff dynamics, and preference function, along with expanded bifurcation analysis. This will strengthen the paper without altering its core claims.

read point-by-point responses

  1. Referee: [Abstract / Model section] Abstract and model formulation: the vector preference is stated to be 'a function of ITN coverage' and host adoption is 'payoff-based,' yet no explicit functional expressions, payoff matrix, or decision dynamics are supplied. Because the direction of the secondary-host prevalence increase, the location of Rc, and the occurrence of the reported bifurcations all depend on these choices, the central claim cannot be assessed for robustness without the precise ODE system.

    Authors: We acknowledge this limitation in the submitted version. The model section describes the structure but leaves the specific forms of the payoff-based adoption dynamics and the ITN-dependent vector preference function unspecified. In revision we will add the explicit functional forms (including the payoff matrix and the differential equation governing ITN adoption rate) together with the full ODE system. These will be chosen to be biologically motivated (e.g., a decreasing saturating function for vector preference shift toward the unprotected host). With the explicit system supplied, readers will be able to reproduce the reported equilibria, Rc threshold, and the counterintuitive prevalence increase. revision: yes

  2. Referee: [Bifurcation analysis] Bifurcation analysis: the conditions for saddle-node and Hopf bifurcations are asserted to arise from the nonlinear coupling, but without the explicit forms of the preference and payoff functions it is impossible to verify whether these bifurcations are structural or artifacts of particular parameterizations of the free functions.

    Authors: We agree that the bifurcation conditions cannot be fully verified without the explicit functions. Upon adding the specific forms, the revised manuscript will derive the Jacobian at the endemic equilibrium and state the precise algebraic conditions (in terms of the model parameters) under which the saddle-node and Hopf bifurcations occur. We will also include numerical continuation results and a brief discussion of how the bifurcations depend on the curvature of the chosen preference and payoff functions, thereby clarifying whether the reported regime shifts are robust within the chosen functional family. revision: yes

Circularity Check

0 steps flagged

No significant circularity; thresholds and bifurcations follow from explicit model dynamics

full rationale

The paper derives R0 and Rc via standard next-generation matrix methods applied to the ODE system parameters. Bifurcation conditions (saddle-node, Hopf) are obtained from the system's Jacobian and characteristic equations under the stated nonlinear coupling. Vector preference and ITN adoption are introduced as explicit modeling choices (functions of coverage and payoff-based decisions), but the reported equilibria, stability, and counterintuitive prevalence shift are consequences of solving the resulting dynamical system rather than tautological redefinitions or fitted outputs renamed as predictions. No self-citations, uniqueness theorems, or ansatzes smuggled via prior work are invoked in the provided text. The derivation chain is self-contained against the model's own equations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the specific nonlinear functional forms chosen for ITN adoption (payoff-based) and vector preference (ITN-coverage dependent); these forms are not detailed in the abstract and function as modeling choices that enable the reported dynamics.

free parameters (1)
  • payoff and preference function parameters
    The nonlinear coupling terms require parameters for perceived costs, infection risks, and preference shifts that are not specified in the abstract and are typically chosen or fitted to illustrate bifurcations.
axioms (1)
  • standard math The transmission dynamics are captured by a deterministic system of ordinary differential equations with continuous time.
    Standard compartmental modeling assumption invoked for equilibrium and bifurcation analysis.

pith-pipeline@v0.9.1-grok · 5761 in / 1298 out tokens · 41416 ms · 2026-07-01T02:13:54.063419+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

  1. [1]

    PLoS One13, 0198280 (2018)

    Mukhtar, A.Y., Munyakazi, J.B., Ouifki, R., Clark, A.E.: Modelling the effect of bednet coverage on malaria transmission in South Sudan. PLoS One13, 0198280 (2018)

    work page 2018

  2. [2]

    BMC Infectious Diseases25, 1707 (2025) 18

    Oraby, T., Tyshenko, M.G., Danquah, I., Bhattacharyya, S.,et al.: Insecticide-treated net use and elimination of malaria in Sub-Saharan African countries: assessing the Global Technical Strategy using an evolutionary game approach. BMC Infectious Diseases25, 1707 (2025) 18

    work page 2025

  3. [3]

    Journal of Theoretical Biology320, 58–65 (2013)

    Agusto, F.B., Del Valle, S.Y., Blayneh, K.W., Ngonghala, C.N., Goncalves, M.J., Li, N., Zhao, R., Gong, H.: The impact of bed-net use on malaria prevalence. Journal of Theoretical Biology320, 58–65 (2013)

    work page 2013

  4. [4]

    Malaria Journal6, 1–12 (2007)

    Le Menach, A., Takala, S., McKenzie, F.E., Perisse, A., Harris, A., Flahault, A., Smith, D.L.: An elaborated feeding cycle model for reductions in vectorial capacity of night-biting mosquitoes by insecticide-treated nets. Malaria Journal6, 1–12 (2007)

    work page 2007

  5. [5]

    Malaria Journal17, 1–11 (2018)

    Stone, C., Gross, K.: Evolution of host preference in anthropophilic mosquitoes. Malaria Journal17, 1–11 (2018)

    work page 2018

  6. [6]

    Proceedings of the Royal Society B: Biological Sciences272, 1669–1675 (2005)

    Bauch, C.T.: Imitation dynamics predict vaccinating behaviour. Proceedings of the Royal Society B: Biological Sciences272, 1669–1675 (2005)

    work page 2005

  7. [7]

    Nonlinear Dynamics113, 28579–28599 (2025)

    Li, L., Xiao, Y.: Effect of behavior change pattern on disease transmission dynamics. Nonlinear Dynamics113, 28579–28599 (2025)

    work page 2025

  8. [8]

    sarkar et al

    Sarkar, T., Srivastava, P.K., Biswas, P.: Modeling dengue with saturated incidence, vacci- nation, and treatment rates: Numerical insights and nonlinear behavior: T. sarkar et al. Nonlinear Dynamics113, 28511–28553 (2025)

    work page 2025

  9. [9]

    Nonlinear Dynamics114, 151 (2026)

    Zhang, S., Xiao, Y.: Analysis on an sis epidemic model with saturated recovery and dynamic behavior changes. Nonlinear Dynamics114, 151 (2026)

    work page 2026

  10. [10]

    Journal of Theoretical Biology342, 39–46 (2014)

    Honjo, K., Satake, A.: N-player mosquito net game: individual and social rationality in the misuse of insecticide-treated nets. Journal of Theoretical Biology342, 39–46 (2014)

    work page 2014

  11. [11]

    Applied Mathematics7, 852–860 (2016)

    Broom, M., Rycht´ ar, J., Spears-Gill, T.: The game-theoretical model of using insecticide- treated bed-nets to fight malaria. Applied Mathematics7, 852–860 (2016)

    work page 2016

  12. [12]

    PLoS Neglected Tropical Diseases 14, 0008833 (2020)

    Han, C.Y., Issa, H., Rycht´ aˇ r, J., Taylor, D., Umana, N.: A voluntary use of insecticide treated nets can stop the vector transmission of chagas disease. PLoS Neglected Tropical Diseases 14, 0008833 (2020)

    work page 2020

  13. [13]

    Royal Society Open Science8, 201960 (2021)

    Fortunato, A.K., Glasser, C.P., Watson, J.A., Lu, Y., Rycht´ aˇ r, J., Taylor, D.: Mathematical modelling of the use of insecticide-treated nets for elimination of visceral leishmaniasis in Bihar, India. Royal Society Open Science8, 201960 (2021)

    work page 2021

  14. [14]

    Royal Society Open Science9, 220685 (2022)

    Laxmi, Ngonghala, C.N., Bhattacharyya, S.: An evolutionary game model of individual choices and bed net use: elucidating key aspect in malaria elimination strategies. Royal Society Open Science9, 220685 (2022)

    work page 2022

  15. [15]

    PLoS Neglected Tropical Diseases16, 0010765 (2022)

    Rycht´ aˇ r, J., Taylor, D.: A game-theoretic model of lymphatic filariasis prevention. PLoS Neglected Tropical Diseases16, 0010765 (2022)

    work page 2022

  16. [16]

    Dynamic Games and Applications12, 133–146 (2022)

    Angina, J., Bachhu, A., Talati, E., Talati, R., Rycht´ aˇ r, J., Taylor, D.: Game-theoretical model of the voluntary use of insect repellents to prevent zika fever. Dynamic Games and Applications12, 133–146 (2022)

    work page 2022

  17. [17]

    PLoS One19, 031131 (2024)

    Davis, C., Javor, E.R., Rebarber, S.I., Rycht´ aˇ r, J., Taylor, D.: A mathematical model of visceral leishmaniasis transmission and control: Impact of ITNs on VL prevention and elimination in the indian subcontinent. PLoS One19, 031131 (2024)

    work page 2024

  18. [18]

    Journal of Theoretical Biology585, 111796 (2024) 19

    Onifade, A.A., Rycht´ aˇ r, J., Taylor, D.: A dynamic game of lymphatic filariasis prevention by voluntary use of insecticide treated nets. Journal of Theoretical Biology585, 111796 (2024) 19

    work page 2024

  19. [19]

    Journal of The Royal Society Interface13, 20150666 (2016)

    Miller, E., Dushoff, J., Huppert, A.: The risk of incomplete personal protection coverage in vector-borne disease. Journal of The Royal Society Interface13, 20150666 (2016)

    work page 2016

  20. [20]

    PLoS One10, 0144173 (2015)

    Birget, P.L., Koella, J.C.: An epidemiological model of the effects of insecticide-treated bed nets on malaria transmission. PLoS One10, 0144173 (2015)

    work page 2015

  21. [21]

    The Journal of Infectious Diseases215, 790–797 (2017)

    Thomsen, E.K., Koimbu, G., Pulford, J., Jamea-Maiasa, S., Ura, Y., Keven, J.B., Siba, P.M., Mueller, I., Hetzel, M.W., Reimer, L.J.: Mosquito behavior change after distribution of bednets results in decreased protection against malaria exposure. The Journal of Infectious Diseases215, 790–797 (2017)

    work page 2017

  22. [22]

    Journal of Mathematical Biology81, 113–158 (2020)

    Enahoro, I., Eikenberry, S., Gumel, A.B., Huijben, S., Paaijmans, K.: Long-lasting insecticidal nets and the quest for malaria eradication: a mathematical modeling approach. Journal of Mathematical Biology81, 113–158 (2020)

    work page 2020

  23. [23]

    Journal of The Royal Society Interface15, 20180166 (2018)

    Demers, J., Bewick, S., Calabrese, J., Fagan, W.F.: Dynamic modelling of personal protection control strategies for vector-borne disease limits the role of diversity amplification. Journal of The Royal Society Interface15, 20180166 (2018)

    work page 2018

  24. [24]

    https://arxiv.org/abs/2604

    Shetgaonkar, S., Sharma, A.: Modeling the impact of host diversity on the evolution of vector feeding preferences and implications for disease control (2026). https://arxiv.org/abs/2604. 27113

    work page 2026

  25. [25]

    Proceedings of the National Academy of Sciences113, 7518–7525 (2016)

    Weitz, J.S., Eksin, C., Paarporn, K., Brown, S.P., Ratcliff, W.C.: An oscillating tragedy of the commons in replicator dynamics with game-environment feedback. Proceedings of the National Academy of Sciences113, 7518–7525 (2016)

    work page 2016

  26. [26]

    Theoretical Population Biology73, 257–263 (2008)

    Hauert, C., Wakano, J.Y., Doebeli, M.: Ecological public goods games: cooperation and bifurcation. Theoretical Population Biology73, 257–263 (2008)

    work page 2008

  27. [27]

    Cambridge University Press, Cambridge, New York (1998)

    Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge, New York (1998)

    work page 1998

  28. [28]

    Journal of the Royal Society Interface7, 873–885 (2010)

    Diekmann, O., Heesterbeek, J., Roberts, M.G.: The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface7, 873–885 (2010)

    work page 2010

  29. [29]

    1Impact of varyingE h1 andmon (a)-(c) strategy composition ofh1 population, and (d)-(f) size of vector population, under different values ofσ h2

    Perko, L.: Differential Equations and Dynamical Systems, Springer (2001) Appendix D Figures 20 Fig. 1Impact of varyingE h1 andmon (a)-(c) strategy composition ofh1 population, and (d)-(f) size of vector population, under different values ofσ h2. In (a)-(c) cream white and black colored regions denote the stability of DFE corresponding toE 03 andE 04. Ligh...

    work page 2001