Taming obstinate spreaders: the dynamics of a rumor spreading model incorporating inhibiting mechanisms and attitude adjustment

This paper proposes and investigates a model for rumor spreading and control which accounts for different attitudes and for a distinct type of variable, related to the strength and effectiveness of rumor inhibiting mechanisms. The control mechanisms essentially amount to budgeting and to adjusting the attitude of spreaders. The existence and stability of the trivial (rumor-free) equilibrium and of the semi-trivial equilibrium are characterized in terms of two threshold parameters which quantify the influence of both categories of spreaders. The existence of a positive (rumor-prevailing) equilibrium is also established, its stability being discussed with the help of a bifurcation theorem. A nonstandard finite difference (NSFD) scheme is devised to construct approximate solutions while preserving their positivity, necessary conditions for the existence of the optimal discrete rumor spreading controls being then established.