Malicious viruses spreading on complex networks with heterogeneous recovery rate

We propose a malicious viruses spreading model on complex networks that considers the effects of the resource contribution of healthy neighbors. Due to the difference in resource amount received from the healthy neighbors, the recovery rate of infected nodes is heterogeneous. Through rigorous theoretical analysis and extensive numerical simulations, we find that the virus spreading can be optimally suppressed if each healthy node contributes equal resource to the infected nodes. There is a maximum outbreak threshold and minimum fraction of infected nodes with the optimal strategy of resource contribution. In addition, we find that in a homogeneous network, the strategy of resource contribution can alter the phase transition. If each healthy node contributes relatively evenly, the phase transition is continuous. Whereas, if the recovery resources of infected nodes is mainly relies on nodes with large or small degrees, there is discontinuous phase transition. In heterogeneous network, there is always continuous phase transition.