Competing Social Contagions with Opinion Dependent Infectivity

TL;DR

This work introduces a two-contagion framework on networks where each agent carries a continuous internal opinion $X\in[-1,1]$ that modulates infection and recovery rates for competing beliefs $s\in\{-1,0,+1\}$, capturing confirmation bias and the illusory truth effect. Through agent-based simulations and a mean-field reduction on $k$-regular networks, the authors reveal an opinion-dependent disease-free manifold and multiple long-term outcomes, including rebound and bias overturning, whose basins of attraction depend on the initial average opinion and contagion prevalence. They derive an SIS-like mean-field system with a reproduction number $R_0$, thresholds $A^{\pm}$, and equilibria that delineate stable regions for the dominant contagion, coexistence, or disease-free states. The study further shows that heterogeneous initial opinions modify the basins of attraction, and external recruitment of spreaders can stabilize one contagion over the other, with practical implications for countering misinformation through prebunking and controlled information interventions.

Abstract

The spread of disinformation (maliciously spread false information) in online social networks has become an important problem in today's society. Disinformation's spread is facilitated by the fact that individuals often accept false information based on cognitive biases which predispose them to believe information that they have heard repeatedly or that aligns with their beliefs. Moreover, disinformation often spreads in direct competition with a corresponding true information. To model these phenomena, we develop a model for two competing beliefs spreading on a social network, where individuals have an internal opinion that models their cognitive biases and modulates their likelihood of adopting one of the competing beliefs. By numerical simulations of an agent-based model and a mean-field description of the dynamics, we study how the long-term dynamics of the spreading process depends on the initial conditions for the number of spreaders and the initial opinion of the population. We find that the addition of cognitive biases enriches the transient dynamics of the spreading process, facilitating behavior such as the revival of a dying belief and the overturning of an initially widespread opinion. Finally, we study how external recruitment of spreaders can lead to the eventual dominance of one of the two beliefs.

Figures (12)

• Figure 1: Infection and recovery rates $\beta(x,s)$ (top) and $\gamma(x,s)$ (bottom) as functions of the opinion $x$ for parameters $\beta_{\text{max}}=1$, $\gamma_{\text{max}}=1$, and $\epsilon=1.5$, for $s = +1$ (solid lines) and $s = -1$ (dashed lines).
• Figure 2: (a) A diagram showing an example interaction network for the agent-based model. Each node has an contagion state $-1$ (red), 0 (white), or $+1$ (blue) (shown as the inner circle). The internal opinion of each node is represented by the color of the outer ring, ranging from $-1$ (red) to $+1$ (blue). (b) An example of how repeated exposures can change the opinion of node $j$ to align with the contagion of node $i$ and the possible transition of node $j$ from susceptible to infected with the $+1$ contagion.
• Figure 3: Examples of the stability of the $(A,0,0)$ equilibrium state, from Eqs. (\ref{['R0p1']}) and (\ref{['R0n1']}), for values of $r_0\in \{0.30,0.67,0.80,1.00 \}$ as a function of $A$ and $\epsilon$. Red represents unstable towards the $-1$ contagion ($R_0^+<1$ and $R_0^->1$), blue represents unstable towards the $+1$ contagion ($R_0^+>1$ and $R_0^-<1$), and white represents stable ($R_0^+<1$ and $R_0^-<1$).
• Figure 4: The long-term behavior of the agent-based model for $r_0\in \{0.30,0.67,0.80,1.00 \}$ as a function of $X(0)$ and $\epsilon$. The color of each point represents which contagion was successful more frequently out of $9$ independent trails of the agent-based simulation on a $30$-regular network of $N=1000$ nodes. Each simulation ran for 3000 time steps with initial fractions of infected nodes given as $(S_+(0),S_-(0))\in \{(0.05i/2,\, 0.05j/2)|\,i\in \{0,1,2\},\,j\in \{0,1,2\} \}$.
• Figure 5: An example of a rebound to the $+1$ endemic state for a single simulation of the agent-based model and single numerical solution to the mean-field equations (\ref{['SP']})-(\ref{['OP']}) with parameters $r_0=0.66$, $K=0.4$, and $\tau=0.07$ on a 7-regular network. The dot-dashed black line indicates the threshold $A^+$ from Eq. (\ref{['AP']}).