How complex behavioural contagion can prevent infectious diseases from becoming endemic

arXiv:2604.10995 · q-bio.PE · Submitted 2026-04-13 · Read on arXiv

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Introduction to the show: ident: Genomics Radio. Generated commentary on the latest computational biology and genomics papers.

Ines: I'm Ines.

Marcus: And I'm Marcus, here with Yuki.

Ines: We're looking at the paper: "How complex behavioural contagion can prevent infectious diseases from becoming endemic".

Marcus: Here's the gist of the paper. Infectious disease transmission in human populations has a complex two-way interaction with changes in host behaviour It is increasingly recognised that incorporating adaptive behavioural change into epidemic models is important for improving understanding of infectious disease dynamics and developing policy-relevant modelling tools An important aspect of behavioural dynamics is social contagion, where people tend to adopt behaviours exhibited by others around them The authors explore an epidemic model with complex behavioural contagion, where the behaviour uptake rate is a nonlinear function of the number of behaving contacts They show that, in some regions of parameter space, the model has multiple disease-free equilibria In this situation, the occurrence of an epidemic in a population with an initially low level of behaviour practice can trigger a self-sustaining increase in behaviour, which then causes the disease to be eliminated They demonstrate that this mechanism of epidemic-triggered uptake of behaviour leading to disease elimination can occur in the presence and absence of temporary post-infection immunity.

Ines: Model Formulation and Dynamics The study considers a modified version of the ‘behaviour and disease model’ proposed in

13: , focusing on an SIS model with behavioural dynamics that are a type of complex social contagion where the behaviour uptake rate depends nonlinearly (in this case quadratically) on the number of contacts who are in the behaving class The model is described by a system of four ordinary differential equations for the proportion of the population in four compartments: non-behaving susceptible (SN), non-behaving infectious (IN), behaving susceptible (SB), and behaving infectious (IB).

Marcus: The force of infection is defined as λ = R0 (IN + (1 − qc)IB) and the rate of behaviour uptake per unit of dimensionless time is ω(S, B) = α / τB squared + χ(1 − S).

Ines: Bifurcation Analysis and Regimes The analysis reveals that complex (nonlinear) contagion of behaviour results in new dynamical regimes, including situations where an initial rise in infections triggers a self-sustaining increase in behaviour that is sufficient to eliminate infection The key bifurcation parameters identified include the basic reproduction number R0, the strength of the behavioural effect on disease transmission, and the speed of behaviour uptake relative to behaviour abandonment.

Paper summary: Ines: So, to quickly recap the main thrust of "How complex behavioural contagion can prevent infectious diseases from becoming endemic," the authors are looking at how host behaviour and disease transmission are coupled in a two-way interaction.

Marcus: They claim that incorporating this adaptive behavioural change into epidemic models is important because it gives us a better view of disease dynamics and helps build tools for policy.

Ines: The core finding is that complex, nonlinear contagion of behaviour results in new dynamical regimes where an initial rise in infections can trigger a self-sustaining increase in behaviour sufficient to eliminate the infection.

Marcus: They show this novel phenomenon can happen regardless of whether the model includes temporary infection-induced immunity, which is a significant detail because it broadens when this dynamic applies.

Yuki: From my perspective, this suggests that even if we start with low levels of behaviour practice, the dynamics aren't fixed; they are sensitive to initial infection events in a complex way that could lead to entirely different long-term states.

Ines: Right. They model this using a modified SIS model where the uptake rate is proportional to B squared instead of just B, which is what creates that complex social contagion mechanism <ref:2604.10995#pg3>.

Marcus: That nonlinear relationship, that dependence on B squared, is what drives the bifurcation analysis they perform, showing how the system can switch between different stable states depending on parameters like R zero and tau.

Yuki: So, when you look at those parameter regions they define, it suggests that the possibility of disease elimination isn't guaranteed; it depends heavily on where your specific population falls within that space.

Ines: That’s right. The analysis classifies ten distinct parameter regions based on R zero and tau, which maps out the different possible outcomes for disease spread in this system <ref:2604.10995#pg3>.

Marcus: It really means that we can't just look at R zero in isolation anymore; we have to consider the interplay between transmission strength, the speed of behaviour uptake, and how fast people abandon it.

Ines: That’s a good summary of what they’re trying to convey about the coupling and nonlinearity in these systems before we get into their specific results.

Conclusion: Ines: So wrapping up this paper, "How complex behavioural contagion can prevent infectious diseases from becoming endemic," the authors are pointing out that this dynamic interaction is what allows for self-sustaining behaviour change to counteract the disease spread.

Marcus: The implication for public health policy is that we should focus on interventions that aim to shift a population past that critical threshold where this kind of sustained behavioural change can happen naturally.

Yuki: So, in simpler terms, it suggests that increasing the visibility of protective behaviour or making non-compliant behaviour socially less acceptable could be a way to push the system into a state where infection self-correction is possible.

Ines: That’s right. The paper argues that this mechanism isn't just about reducing transmission directly; it's about a feedback loop where behaviour changes because of disease pressure, and that pressure then causes more behaviour changes <ref:2604.10995#pg16>.

Marcus: It really highlights the idea that persistent behaviour change driven by epidemics can be a factor in controlling things like sexually transmitted infections, which is a real-world application we should keep an eye on.

Yuki: That persistence is what makes me wonder about the long-term stability of these changes; we need to know if this sustained high behaviour settles into a new equilibrium or if it's just temporary compliance.

Ines: And that’s exactly where future research needs to focus, because understanding how long this self-sustaining high behaviour lasts is crucial for translating these mathematical models into real public health action.

School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand · Te P¯unaha Matatini, Auckland, New Zealand · School of Mathematical Sciences, Adelaide University, Adelaide, Australia · CSIRO

q-bio.PE

Submitted: 2026-04-13

Updated: 2026-10-28

Code: https://github.com/michaelplanknz/behaviour_and_disease_SIS_model

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 77/100

The gist: Infectious disease transmission in human populations has a complex two-way interaction with changes in host behaviour It is increasingly recognised that incorporating adaptive behavioural change into

Key concepts

Complex Behavioural Contagion: This is a type of social contagion where people adopt behaviors based on how many contacts are already exhibiting that behavior. The uptake rate is not simple; it depends nonlinearly on the number of people around you who are already behaving a certain way, leading to richer, more dynamic changes in population behavior.
Disease-Free Equilibria (DFE): These are stable states in the model where the disease is completely absent from the population. The analysis showed that depending on parameters like the speed of behavior uptake ($ au$), there can be multiple DFE scenarios, including one where no one practices any behavior at all.
Epidemic-Triggered Uptake: This novel mechanism describes a situation where an epidemic causes people to change their behavior in a way that ultimately stops the epidemic. This requires that the rate of adopting protective behavior is fast enough relative to when people stop practicing it, and the behavior must be strong enough to reduce transmission.

Terminology

Dynamical regimes — 3× in this paper · explained in 2 episodes
Bifurcation Analysis — 2× in this paper · explained in 2 episodes
Feedback Loop — 2× in this paper · explained in 2 episodes
Adam — 1× in this paper · explained in 3 episodes
Core — 1× in this paper · explained in 2 episodes
EMMA — 1× in this paper · explained in 2 episodes
Generalization — 1× in this paper · explained in 14 episodes
Structural Properties — 1× in this paper · explained in 2 episodes

Summary

Infectious disease transmission in human populations has a complex two-way interaction with changes in host behaviour It is increasingly recognised that incorporating adaptive behavioural change into epidemic models is important for improving understanding of infectious disease dynamics and developing policy-relevant modelling tools An important aspect of behavioural dynamics is social contagion, where people tend to adopt behaviours exhibited by others around them The authors explore an epidemic model with complex behavioural contagion, where the behaviour uptake rate is a nonlinear function of the number of behaving contacts They show that, in some regions of parameter space, the model has multiple disease-free equilibria In this situation, the occurrence of an epidemic in a population with an initially low level of behaviour practice can trigger a self-sustaining increase in behaviour, which then causes the disease to be eliminated They demonstrate that this mechanism of epidemic-triggered uptake of behaviour leading to disease elimination can occur in the presence and absence of temporary post-infection immunity.

Model Formulation and Dynamics

The study considers a modified version of the ‘behaviour and disease model’ proposed in [13], focusing on an SIS model with behavioural dynamics that are a type of complex social contagion where the behaviour uptake rate depends nonlinearly (in this case quadratically) on the number of contacts who are in the behaving class The model is described by a system of four ordinary differential equations for the proportion of the population in four compartments: non-behaving susceptible (SN), non-behaving infectious (IN), behaving susceptible (SB), and behaving infectious (IB). The force of infection is defined as λ = R0 (IN + (1 − qc)IB) and the rate of behaviour uptake per unit of dimensionless time is ω(S, B) = α / τB squared + χ(1 − S).

Bifurcation Analysis and Regimes

The analysis reveals that complex (nonlinear) contagion of behaviour results in new dynamical regimes, including situations where an initial rise in infections triggers a self-sustaining increase in behaviour that is sufficient to eliminate infection The key bifurcation parameters identified include the basic reproduction number R0, the strength of the behavioural effect on disease transmission, and the speed of behaviour uptake relative to behaviour abandonment. The paper classifies ten distinct parameter regions based on the values of R0 and τ, showing how dynamics change across these regimes For instance, when the social behaviour uptake rate is low (τ < 4), the only disease-free equilibrium is that with no behaviour (the NDFE). When τ > 4, there are three disease-free equilibria: one with no behaviour and two with positive behaviour

Key Findings on Disease Elimination

The analysis demonstrates that the occurrence of an epidemic drives an increase in behaviour that subsequently causes the disease to die out, a novel phenomenon possible only in models with complex behavioural contagion This mechanism requires that behaviour uptake is sufficiently fast relative to behaviour abandonment and behaviour has a sufficiently strong impact on transmission. Furthermore, this outcome can only occur if high levels of behaviour are self-sustaining following the epidemic, as behavior lapses once the epidemic is over, the disease may re-invade once the susceptible population is large enough.

Implications for Public Health Policy

The analysis highlights that public health interventions aimed at strengthening social norms around protective behaviour could shift a population across a critical threshold, suggesting that increasing the visibility of compliant behaviour or reducing the social acceptability of abandoning it could qualitatively improve the long-term disease outcome <ref:2604.10995#pg16> The critical threshold is identified as τ = 4, below which only zero behaviour is present in the disease-free equilibrium, while above it, self-sustaining high-behaviour equilibria emerge.

Model Generalizations

The authors suggest several ways the model could be generalized, including exploring a situation where behaviour reduces disease transmission by reducing susceptibility and/or contagiousness <ref:2604.10995#pg17> They also note that the model and that of [13] assume that behavioural change is independent of disease state, which may not always be true as infectious individuals may be more (or less) likely than susceptible individuals to adopt the behaviour depending on the context <ref:2604.10995#pg17> The uptake and abandonment rates could also be general polynomials with a mixture of linear and nonlinear terms in both the prevalence of behaviour B and the prevalence of disease I <ref:2604.10995#pg17>

SIRS Model Comparison

The SIRS model, which includes temporary immunity, exhibits similar disease-free equilibria and stability properties to the SIS model. The authors demonstrate that there are parameter values for which the SIRS model also exhibits one of the key phenomena shown by the SIS model, namely an epidemic followed by extinction of the disease due to persistent high behaviour.

Numerical Validation

The results are validated through numerical simulations, with code to reproduce the results being publicly available <ref:2604.10995#pg21> All analyses were run in Matlab R2022b. The dynamics of the susceptibility-modulated model show qualitative similarities to the transmission-modulated model, with the prevalence of behaviour being higher among the susceptible class than in the population as a whole. The SIRS model solutions show that when behaviour is included in the model, the first epidemic wave is reduced in size and there are no subsequent waves, leading to disease extinction.

Conclusion on Persistence

The analysis reveals evidence of persistent behaviour change driven by epidemics, noting that some behaviours induced by the Covid-19 pandemic showed signs of persistence This is reminiscent of the authors' results indicating a shift in attitudes and behavioural compliance after epidemic outbreaks, even when infection is eliminated. The sustained behaviour change has also been proposed as an important factor in the control of sexually transmitted infections.

Summary of Key Findings

The presence of complex contagion means that, in some situations, the occurrence of an epidemic drives an increase in behaviour that subsequently causes the disease to die out <ref:2604.10995#pg16> The model shows that higher values of R0 may lead to behaviour-driven disease elimination, contrasting with classical models where higher R0 usually worsens outcomes. This phenomenon requires both τ > 4 and sufficiently large qc for the outcome to occur.

Final Statement

The paper explores a simplified model of infectious disease transmission in the presence of dynamic behavioural change, which reduces the susceptibility and/or contagiousness of those adopting the behaviour. The analysis reveals that the presence of complex contagion means that, in some situations, the occurrence of an epidemic drives an increase in behaviour that subsequently causes the disease to die out <ref:2604.

Improvements for AI systems

Adaptive Epidemic Control Modeling: The improved AI system can simulate scenarios where an epidemic triggers a self-sustaining increase in behavior sufficient to cause disease elimination, as described by the occurrence of an epidemic in a population with an initially low level of behaviour practice can trigger a self-sustaining increase in behaviour, which then causes the disease to be eliminated.
Bifurcation Parameter Optimization: The system can use the identified key bifurcation parameters R0, the strength of behavioural effect on disease transmission, and the speed of uptake relative to abandonment to predict whether an outbreak will lead to endemicity or behavior-driven elimination based on parameter space regions.
Policy Recommendation Engine: The AI can generate policy recommendations by mapping observed epidemiological states (e.g., regime 7 or regime 8) to specific behavioral interventions, such as increasing visibility of compliant behavior, aiming to shift the population across critical thresholds like τ = 4 or R0,T C+.

Abstract

Infectious disease transmission in human populations has a complex two-way interaction with changes in host behaviour. It is increasingly recognised that incorporating adaptive behavioural change into epidemic models is important for improving understanding of infectious disease dynamics and developing policy-relevant modelling tools. An important aspect of behavioural dynamics is social contagion, where people tend to adopt behaviours exhibited by others around them. In a simple behavioural contagion model, the behaviour uptake rate increases linearly with the number of contacts who have adopted a given behaviour. Here, we explore an epidemic model with complex behavioural contagion, where the behaviour uptake rate is a nonlinear function of the number of behaving contacts. We identify key bifurcation parameters of the model, which include the basic reproduction number R 0, the strength of the behavioural effect on disease transmission, and the speed of behaviour uptake relative to behaviour abandonment. We show that, in some regions of parameter space, the model has multiple disease-free equilibria. In this situation, the occurrence of an epidemic in a population with an initially low level of behaviour practice can trigger a self-sustaining increase in behaviour, which then causes the disease to be eliminated. In some cases, while moderate values of R 0 lead to the disease becoming endemic, higher values of R 0 may lead to behaviour-driven disease elimination. We demonstrate that this mechanism of epidemic-triggered uptake of behaviour leading to disease elimination can occur in the presence and absence of temporary post-infection immunity.