The invasive and disruptive spreading of rumors and other malicious types of false or partly false messages are a sad yet pervasive reality on the major social networks platforms.
To better mathematically understand this phenomenon, the authors propose both a deterministic and a stochastic class-age-structured rumor propagation models.
First, the authors characterize the deterministic rumor propagation model by a coupled system of ordinary and partial differential equations. The positivity and boundedness of solutions are proved, and the basic reproduction number is derived. Second, the stochastic rumor propagation model is formulated by means of stochastic differential equations. The existence of global positive solutions in model is analysed using Itô’s formula and the stochastic Lyapunov function. Additionally, by utilizing the comparison principle of stochastic differential equations and the strong law of large numbers, several sufficient conditions for extinction and persistence of the rumor are derived. Finally, numerical simulations are carried out for illustrating the results.
The paper would have profited by a better language editing.