Opinion-Driven Vaccination and Epidemic Dynamics on Heterogeneous Networks

Abstract

Vaccination campaigns play a pivotal role in controlling infectious diseases. Their success, however, depends not only on vaccine efficacy and availability but also significantly on public opinion and the willingness of individuals to vaccinate. This paper investigates a coupled opinion-epidemic model on heterogeneous networks, where individual opinions influence vaccination probability, and opinions themselves evolve through a combination of peer interaction and local risk perception derived from observed infection rates. Embedding the coupled dynamics in scale-free networks, particularly barabasi-Albert structures, allows us to examine the role of network heterogeneity beyond homogeneous-mixing assumptions. Using Monte Carlo simulations and a semi-analytical microscopic Markov-chain approach, we derive and numerically validate analytical expressions for the critical infection threshold and stable vaccinated population where risk perception dominated peer influence. Our results show that stronger local risk perception enhances pro-vaccination opinions and suppresses infection, while dominant peer influence can increase long-term infection levels. These findings underscore the importance of accounting for social behavior and network structure when designing effective vaccination and epidemic control strategies.

Figures (8)

• Figure 1: Schematic representation of the coupled SIV model with opinion-dependent vaccination. Susceptible ($S$) individuals can become infected ($I$) or vaccinated ($V$). Infected nodes recover with rate $\alpha$, and vaccinated nodes lose immunity with rate $\phi$. Opinion $O_i$ influences vaccination probability $\gamma_i$.
• Figure 2: Steady-state average opinion ($O_{\infty}$), fraction infected ($I_{\infty}$), and fraction vaccinated ($V_{\infty}$) as functions of the infection rate $\lambda$ (with parameters $\alpha = 0.4$, $\epsilon = 0.5$, $\omega = 0.8$, and $\phi = 0.01$). For each $\lambda$, 50 realizations were performed for both the MC and analytical models. Individual MC realizations are shown as light blue dots, with their mean trend indicated by the solid blue line. Similarly, analytical results are represented by light red crosses, and their mean trend by the solid red line. The theoretical infection threshold, $\lambda_c \approx 0.0155$ (derived in Section \ref{['Semi-analytical_MMCA']}), is marked on the $I_{\infty}$ plot. For further discussion on the temporal behaviour of these variables, please refer to the appendix \ref{['TS_dynamics']} (Fig. \ref{['fig:timeseries_infection']}) .
• Figure 3: Phase diagrams showing the steady-state infection density ($I_{\infty}$) across varying infection rates ($\lambda$) and recovery rates ($\alpha$). The left panel shows the MC-derived final state, while the right panel uses the semi-analytical model. Both plots fix $\omega=0.8, \phi=0.01, \epsilon=1.0$ The theoretically obtained critical threshold $\lambda_c$ is shown with dashed line.
• Figure 4: Impact of peer influence ($\epsilon$) and risk perception ($\omega$) on steady-state outcomes.Top row (a, b, c): Heatmaps showing the steady-state fraction of infected individuals ($I_{\infty}$), vaccinated individuals ($V_{\infty}$), and average opinion ($O_{\infty}$) across the $(\omega, \epsilon)$ parameter space. Parameters are fixed at $\alpha=0.7$, $\phi=0.01$, and $\lambda=0.6$. Two distinct regimes are marked: the white circle represents a high-conformity, low-risk perception state $(\omega=0.2, \epsilon=0.8)$, while the white cross represents a low-conformity, high-risk perception state $(\omega=0.8, \epsilon=0.2)$. Bottom rows: Panels (d, e, f) and (g, h, i) show detailed sweeps for the parameter sets marked by the circle and cross, respectively. These panels display the steady-state metrics ($I_\infty$, $V_\infty$, $O_\infty$) from left to right as a function of the infection rate $\lambda$. In the high-conformity regime (circle), strong peer influence suppresses the behavioral response, preventing effective vaccination and allowing infection to persist even at low $\lambda$. In contrast, the high-risk perception regime (cross) shows that risk awareness drives a rapid shift to a pro-vaccine consensus ($O_\infty \approx 1$), effectively suppressing the epidemic across a wider range of transmission rates.
• Figure 5: Verification of the analytical saturation coverage. The steady-state vaccination coverage $V_\infty$ is plotted against the waning rate $\phi$. The dashed line represents the theoretical prediction $V_\infty = \frac{1}{1+\phi}$ derived in Eq. \ref{['eq:V_analytical_saturation']}, while the points represent MC simulation results, showing excellent agreement. This was generated for fixed parameters $\alpha=0.1, \epsilon = 0.05, \omega = 0.9$ and $\lambda = 0.2$, with averages done over $100$ runs for each parameter set.