Global attractivity and optimal dynamic countermeasure of a virus propagation model in complex networks

This paper aims to study the combined impact of countermeasure and network topology on virus diffusion and optimal dynamic countermeasure. A novel heterogenous propagation model and its optimal control problem are proposed and analyzed. Qualitative analysis shows that the unique equilibrium of the proposed model is globally attractive and the optimal control problem has an optimal control. Some simulation experiments are also performed. Specifically, it is found that our obtained results are contrary to some previous results and countermeasure dissemination to higher-degree nodes is more effective than that to lower-degree nodes. The related explanations are also made. This indicates that countermeasures and network topology play an important role in suppressing viral spread.