Coupling opinion dynamics and epidemiology

This research investigates the coupled dynamics of behavior and infectious disease using a mathematical model. We integrate a two-state q-voter opinion process with SIS-type infection dynamics, where transmission rates are influenced by the opinion and an infection-induced switching mechanism represents individuals reassessing their behavior upon infection. Analytically, we derive conditions for the stability of endemic and disease-free equilibria. Numerical simulations reveal complex dynamics: above a certain infectivity threshold, the system can exhibit alternative basins of attraction leading to a balanced endemic fixed point or stable limit cycles. Notably, the dominant asymptotic opinion and resulting epidemiological outcomes show non-monotonic relationships with infectivity, highlighting the potential for adaptive behavior to induce complex system dynamics. These findings underscore the critical role of social interventions; shifts in behavioral norms and trust can permanently alter epidemic outcomes, suggesting that such interventions are as crucial as biomedical controls

💡 Research Summary

This paper presents a coupled mathematical model that integrates a two‑state q‑voter opinion dynamics with a classic SIS (susceptible‑infected‑susceptible) epidemic framework. Individuals hold either opinion A (low protective behavior) or opinion B (high protective behavior). Opinion changes follow the q‑voter rule: a focal individual switches only when it encounters q neighbors all holding the opposite opinion, with a symmetric switching rate p. The epidemic component assumes that infected individuals with opinion A transmit the disease at rate β, while those with opinion B transmit at a reduced rate αβ (0 ≤ α ≤ 1). An additional key mechanism is that any infection forces the individual to switch opinions, representing a reassessment of behavior after experiencing disease. Recovery occurs at a constant rate γ, independent of opinion.

After nondimensionalising time by the recovery period, the basic reproduction number R = β/γ and the scaled opinion‑switching rate p = \tilde p/γ become the principal control parameters. The full system is four‑dimensional (SA, SB, IA, IB) but can be reduced to three dimensions using the variables x = SA, y = SB, and v = IA + αIB, or alternatively to (s, z, v) where s = x + y (total susceptibles) and z = αx + y (a weighted susceptible mix).

The authors first analyse disease‑free equilibria (DFE). Three DFEs exist: DFE0 = (0, 1, 0) (all B), DFE1 = (1, 0, 0) (all A), and a symmetric DFEb = (½, ½, 0). Linearisation shows that DFE0 is stable when R < 1, DFE1 is stable when R < 1/α (and for α = 0 it is always stable), while DFEb is unstable for any positive R.

Endemic equilibria are more intricate. A “balanced” endemic equilibrium EEb has equal fractions of A and B susceptibles (x = y = 1/