Partial differential equation modeling of malware propagation in social networks with mixed delays

Abstract

With the wide applications of social networks, government and individuals increasingly emphasize information networks security. This paper is devoted to investigating a reaction–diffusion malware propagation model with mixed delays to describe the process of social networks. Applying matrix theory for characteristic values, we establish the local stability conditions of a positive equilibrium point. Based on the linear approximation method of nonlinear systems, the Hopf bifurcation at the positive equilibrium point is considered. Additionally, we identify some sensitive parameters in the process of malware propagation that are significant for control theory. Finally, numerical simulations are performed to illustrate the theoretical results.