I2E2S2R Rumor Spreading Model in Homogeneous Network with Hesitating and Forgetting Mechanisms

TL;DR

The paper addresses rumor spreading when two information streams propagate on a homogeneous network, introducing an SEIR-like I2E2S2R model with hesitating and forgetting mechanisms. It derives the basic reproduction number $\mathcal{R}_0=\max\{\mathcal{R}^1_0,\mathcal{R}^2_0\}$ and proves global stability of the rumor-free equilibrium for $\mathcal{R}_0<1$, plus a global-stability result for a prevailing equilibrium under a simplifying condition. An optimal-control formulation with four strategies is analyzed via Pontryagin's Maximum Principle, including explicit control laws, and existence is established. Numerical simulations demonstrate how network connectivity and awareness measures shape rumor dynamics and show the effectiveness of the proposed control strategies, especially when applied early.

Abstract

The spreading and controlling of rumors have great impacts on our society. The transmission of infectious diseases and the spreading of rumors have some common scenarios. Like cross-infection propagation of diseases, two or many kinds of rumors or information may spread at the same time. In this paper, we propose a novel I2E2S2R rumor-spreading model in a homogeneous network. The rumor-free equilibrium, as well as the basic reproduction number, have been calculated from the mean-field equations of the model. Lyapunov function and the LaSalle invariance principle are used to establish the global stability of the rumor-free equilibrium. In numerical simulations, it is perceived that a higher degree of network helps to spread rumors quickly. We have also found that making people aware can help to disappear rumors faster from the network. In addition, making people divert from the rumor to exact information can lessen the spreading of the rumor.

Figures (11)

• Figure 1: The schematic diagram of the I2E2S2R model for the rumor spreading process.
• Figure 2: The curves of the density of the seven classes over time(t)
• Figure 3: The curves of the density of $E_1, E_2, S_1$ and $S_2$ for different $\lambda_1$.
• Figure 4: The curves of the density of $E_1, E_2, S_1, S_2, R_1$ and $R_2$ for different $\gamma$ and $\psi$.
• Figure 5: The curves of the density of $E_1, E_2, S_1$ and $S_2$ over time with different $\sigma$.