A Mathematical Model for Rumor Propagation Considering Awareness Effect - Venn Yan Ishak Ilwaru; Lazarus Beay; Lusye Bakarbessy; Maryone Saija; Meilly Silalily; Serli Ilela (Department of Mathematics, Universitas Negeri Gorontalo, 2026)
Nowadays, the prevalence of social networks in our societies is well-established, as are their positive and negative implications. The effect of misinformation can lead to detrimental consequences in various aspects of life. This emphasizes the importance of proper control over information. Next, we present a new rumor model in this publication, distinguished by its consideration of irresolute individuals. A basic reproduction number (R0) is the threshold for rumor propagation, which is determined through a next-generation matrix approach. Additionally, we utilize the Jacobian matrix method alongside Lyapunov stability theory to provide a rigorous proof for the local and global asymptotic stability of both the rumor-free and rumor equilibria. The analysis results show that the rumor-free equilibria will be locally and globally stable for R0 < 1, and vice versa. Any change in the parameters of human consciousness (v) or human unconsciousness (w) significantly affects population dynamics. Moreover, a set of numerical simulation experiments and the subsequent analysis of their results are presented to validate the effectiveness of the model under consideration. Finally, the effects of various parameters within the proposed model have been examined.