A novel approach in controlling the spread of a rumor within a crowd

The spread of rumors within a crowd can lead to harmful consequences, ranging from misinformation and social disturbances to public panic and injuries or fatalities. In this work, we propose a novel approach to an effective strategy for reducing the number of individuals affected by a rumor within a crowd. This strategy relies on developing control functions operating between zero and one, ensuring that the number of individuals affected by the rumor remains below a predetermined threshold at any given time. We analyze this strategy within the frameworks of continuous-time and discrete-time SIR models, which divide the population into Susceptible (S), Infectious (I), and Recovered (R) individuals, considering both practical constraints and theoretical limitations. Our results demonstrate that the proposed control functions ensure a gradual decrease in the number of affected and susceptible individuals over time, effectively limiting the spread of rumors and preventing uncontrollable situations. Numerical simulations illustrate the efficiency of this approach, highlighting its ability to achieve specific objectives in real-world scenarios.