Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks

Abstract

This paper is devoted to investigating a novel susceptible-exposed-infected-recovered (SEIR) delayed rumor propagation model with saturation incidence on heterogeneous networks. Firstly, by analyzing the corresponding mean-field equations of this model, the basic reproduction number R0 and the rumor-spreading equilibrium are obtained. Secondly, by utilizing the delay differential equations theorem and constructing the appropriate Lyapunov function, the global stability of the rumor equilibriums are proved in detail. Thirdly, optimal control strategy is proposed and analyzed by utilizing the Pontryagin’s Minimum Principle, which is to reduce the relative density of the rumor-spreading individuals and relevant costs. Finally, some numerical examples are used to demonstrate the validity of the derived results.