Abstract
In this paper, a new rumor spreading model in social networks has been investigated. We propose a new version primarily based on the cholera model in order to take into account the expert pages specialized in the dissemination of rumors from an existing IRCSS model. In the second part, we recommend an optimal control strategy to fight against the spread of the rumor, and the study aims at characterizing the three optimal controls which minimize the number of spreader users, fake pages, and corresponding costs; theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.
Highlights
In this paper, a new rumor spreading model in social networks has been investigated
We recommend an optimal control strategy to fight against the spread of the rumor, and the study aims at characterizing the three optimal controls which minimize the number of spreader users, fake pages, and corresponding costs; theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle
We propose a new model which describes the dynamics of rumor spread through social media based on the cholera model [22] and combine it with the previous work model by adding new cubicles P which represent the page’s rumor
Summary
We consider a discrete mathematical model ISpStP that will describe the dynamics of a population of rumors; our model consists of four compartments representing the subdivision of the population that reacts in the spread of the rumor in a social network: I: ignorant, users who do not know the rumor and susceptible to be informed. Us, we have an incoming flux which equals to θ(αhSpI + αeI(P/κ + P)) which represents the proportion of the new users who will spread the rumor. Is number increases at a rate (1 − θ)(αhSpI + αeI(P/κ + P)) which represents the portion of users who knew that the information is wrong, in addition to the flux that left the Sp compartment Sp(cSp + λSt) + βSp, and decreases with the rate μ1St of stiflers who have deactivated their accounts. (1 – θ) (αh + αe (P/κ + P)) Figure 1: Description diagram of the rumor dynamics
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