Mathematical modeling study demonstrates how stochastic noise alters rumor transmission thresholds in networked populations, highlighting effective media-debunking control strategies.
Key Points
To establish the long-term stochastic dynamics, threshold behavior, and optimal media-debunking control for a rumor transmission model with saturated incidence and environmental noise.
Formulated a stochastic susceptible–infected–hesitating–removed (SIHR) rumor model incorporating Hill-type saturated incidence, Brownian perturbations, and a post-spreading verification state.
Derived a corrected stochastic local reproduction number via Itô calculus and proved positive Harris recurrence and ergodicity using a Foster–Lyapunov framework with the full diffusion covariance matrix.
Designed an optimal media-debunking control using the stochastic maximum principle and evaluated drift-level open-loop schedules with 95% confidence bands and stationary-density diagnostics.
Derived an Itô-corrected stochastic reproduction number that accounts for the second moment of the susceptible boundary process and common attrition noise.
Proved positive Harris recurrence, uniqueness of the invariant probability measure, and global attraction to an endemic state when R0 > 1 under explicit dissipativity conditions.
Demonstrated through simulations that open-loop media-debunking interventions reliably suppress rumor spreading and maintain stability under strong saturation and stochastic noise.