Propagation Dynamics of an Epidemic Model with Heterogeneous Control Strategies on Complex Networks

Complex network theory involves network structure and dynamics; dynamics on networks and interactions between networks; and dynamics developed over a network. As a typical application of complex networks, the dynamics of disease spreading and control strategies on networks have attracted widespread attention from researchers. We investigate the dynamics and optimal control for an epidemic model with demographics and heterogeneous asymmetric control strategies (immunization and quarantine) on complex networks. We derive the epidemic threshold and study the global stability of disease-free and endemic equilibria based on different methods. The results show that the disease-free equilibrium cannot undergo a Hopf bifurcation. We further study the optimal control strategy for the complex system and obtain its existence and uniqueness. Numerical simulations are conducted on scale-free networks to validate and supplement the theoretical results. The numerical results indicate that the asymmetric control strategies regarding time and degree of node for populations are superior to symmetric control strategies when considering control cost and the effectiveness of controlling infectious diseases. Meanwhile, the advantages of the optimal control strategy through comparisons with various baseline immunization and quarantine schemes are also shown.