Adaptive behaviors neutralize bistable explosive transitions in higher-order contagion

Abstract

During contagion phenomena, individuals perceiving a risk of infection commonly adapt their behavior and reduce their exposure. The effects of such adaptive mechanisms have been studied for processes in which pairwise interactions drive contagion. However, contagion and the perception of infection risk can also involve ("higher-order") group interactions, leading potentially to new phenomenology. How adaptive behavior resulting from risk perception affects higher-order processes remains an open question. Here, we consider the impact of several risk-based adaptive behaviors on pairwise and higher-order contagion processes, using numerical simulations and an analytical mean-field approach. For pairwise contagion, adaptive mechanisms based on local (pairwise or group-based) risk perception impact only the endemic state, without affecting the epidemic phase transition. For higher-order contagion processes, instead, the adaptivity defuses the impact of non-linear group interactions: this reduces or even completely suppresses the parameter range in which bistability is possible, effectively transforming a higher-order contagion process into a pairwise one.

Figures (3)

• Figure 1: Schematic representation of contagion and adaptation mechanisms.a: example of a hypergraph $\mathcal{H}$ and the corresponding weighted projected graph $\mathcal{G}$. b: the SIS contagion mechanisms for the node $i$, with pairwise (bottom) and higher-order (top) processes. c: adaptive strategies for node $i$, with group-based awareness (top, $ng$ with $\theta=0.3$: $f_i^{ng}(t)=3/\langle D \rangle$) or pairwise-based awareness (bottom, $nn$: $f_i^{nn}(t)=4/\langle k \rangle$).
• Figure 2: Phase diagram for pairwise and higher-order contagion processes.a, b: the epidemic prevalence in the asymptotic steady state, $I_{\infty}$, as a function of the effective infection rate $r$, for the non-adaptive case (NAD) and for the two adaptation strategies ($nn$, $ng$), respectively for the pairwise and higher-order contagion process. Lines give the results of the numerical integration of the IBMF equations, and markers show the results of numerical simulations. For the higher-order processes, we consider simulations and numerical integration starting either with a low (triangles and dashed lines) or with a high (dots and solid lines) fraction of infected nodes. We consider as substrate a dataset describing interactions in a hospital and the numerical results are averaged over $300$ simulations. Here $\nu=4$, $\theta=0.3$. The insets represent a zoom on the mean-field results in the area marked by a dashed rectangle, and the vertical line indicates $r_C^{NAD,p}$. Note that the error-bars on numerical simulations are smaller than the corresponding markers (considering one standard deviation).
• Figure 3: Neutralization of higher-order contagion. Probability $\langle \chi_e^{i_e>1} \rangle_m$ that a group of size $m$ with at least one susceptible node has more than $1$ infected individuals in the asymptotic steady state, as a function of the effective infection rate $r$, for different values of $m$. $\langle \chi_e^{i_e>1} \rangle_m$ is estimated through numerical integration of the mean-field equations, with initial conditions having high fraction of infected nodes. Panel a corresponds to the non-adaptive case, and panels b,c each to an adaptive strategy. We use $\nu=4$ and $\theta=0.3$, the vertical line indicates $r_C^{NAD,p}$ and the light-blue colored area indicates the bistability region. The inset shows the probability $\rho$ that a group of arbitrary size supports higher-order contagion (light-blue area), i.e., a contagion event triggered by more than one infectious, as a function of $r$, and the complementary probability that it supports pairwise contagion (orange area), see Appendix for how to compute $\rho$.