Mathematical modeling of containing a rumor via counter-rumor

Résumé

The spread of rumors, amplified by digital social networks, represents an increasing challenge for social cohesion, public health, and democratic stability. In this work, we propose a deterministic mathematical model of the epidemic type describing the coupled dynamics of a rumor and a counter-rumor within a homogeneous population. The model, structured into five compartments : ignorant, acceptor, spreader, counter-rumor spreaders, and educated allows us to analyze the conditions under which a rumor can persist or be eradicated. We derive the basic reproduction number $R_0$ and prove the existence of a rumor-free equilibrium. Using Lyapunov functions together with applying LaSalle’s invariance principle, we establish the global asymptotic stability of this equilibrium under appropriate conditions on the model parameters. The model is then enhanced by incorporating three control
policies, such as critical thinking education, awareness program and legal action to mitigate the dissemination of rumor. Sensitivity analysis and parameter estimation are conducted with least squares and extended Kalman filter methods with data collected during Hurricane Harvey in 2017. These steps make it possible to calibrate the model and to carry out numerical simulations that clearly show how different control strategies influence the evolution of each compartment, as well as the variations observed on an hourly time scale. Overall, the results indicate that mathematical modeling provides a useful and reliable framework for supporting the design of intervention strategies aimed at limiting the spread of rumors in highly interconnected societies.