Study Of Two Kinds Of Propagation Behavior Through Optimal Control Approach

The dynamics of network communication,including the spread of infectious diseases in groups,computer virus on the Internet,the spread of rumors spread in social networks,and other public information dissemination and its dynamics,etc.Over a variety of based on the group and spread of the Internet behavior is homogeneous medium network and one of the basic research contents of complex networks.In recent years,this topic is popular in economic activities.This paper will use the method of network propagation dynamics to study two typical types of propagation behavior:(1)Rumor propagationThe wide spread of a false rumor could cause huge losses.Isolating some rumor spreaders is an effective approach to limiting the spread of the rumor,at the cost of violating human rights.This paper focuses on developing an isolation-conversion strategy to minimize the impact of the rumor.Based on a novel rumor-truth mixed spreading model,we measure the impact of the rumor.On this basis,we model the isolation-conversion problem as an optimal control problem.We use the ponte aurous principle of minimum value proved that the problem is the existence of the optimal control.Besides,we present the optimality system for solving the optimal control problem.We give some optimal isolation-conversion strategies by solving the corresponding optimality systems.To our knowledge,this is the first time the isolation-conversion problem is treated in this way.We have done a series of numerical experiments,and given the solutions of the optimality system under the scale-free network,real network and small world network,and compared with the static control,in addition,the parameters in the propagation model.After discussion,some of the conclusions can be used in practice.(2)Viral marketingViral marketing has been one of the main marketing modes.However,theoretical study of viral marketing is still lacking.This paper focuses on the problem of developing a cost-effective dynamic discount pricing strategy for a viral marketing campaign.First,based on a novel word-of-mouth propagation model,we model the original problem as an optimal control problem.Second,We use the ponte aurous principle of minimum value proved that the problem is the existence of the optimal control.Besides,we present the optimality system for solving the optimal control problem.Next,we solve some optimal control models to get their respective optimal dynamic discount pricing strategies.Finally,we examine the effect of some factors on the maximum marketing profit.These results contribute to gaining insight into viral marketing.We have done a series of numerical experiments,and given the solutions of the optimality system under the scale-free network,real network and small world network,and compared with the static control,in addition,the parameters in the propagation model.After discussion,some of the conclusions can be used in practice.