Study Of Immunization Schemes For Infectious Diseases On Directed Networks

The prevalence of infectious diseases has caused enormous damage to human health.Historically,the outbreak of malignant infectious diseases has taken away hundreds of mil-lions of lives.Therefore,it is of great significance to study the immunization strategy of infectious diseases.The combination of complex network theory and infectious disease dynamics makes the study of infectious disease transmission mechanisms more close to reality.In order to better study and immunize infectious diseases,we have studied the im-munization strategy of disease based on the average field theory,degree distribution and threshold theory on the infectious disease model of the directed scale-free network on the basis of predecessors.The main work includes the following aspects:Considering the SIS model with birth and death under the constant and linear node's infectivity.We analyzed the model's critical epidemic threshold and disease-spreading e-quilibrium point on the directed network,and applied proportional immunization,acquain-tance immunization and targeted immunization to the model.We proved that immunization strategies can increase the epidemic thresholds and compared the effectiveness of different immunization strategies under the same average immunization rate.Finally,the optimal control strategy is analyzed on this model,and the existence of the optimal control strategy is proved and the final optimal control system is given.Researching the infectivity of nodes on directed networks,and proposing a new node infectivity function related to both in-degrees and out-degrees.Based on the node's infectiv-ity,the epidemic thresholds for constant,linear,and nonlinear infectivity of the traditional SIS model on a directed scale-free network were calculated.Studying the targeted immunization strategy on directed networks.We divided the traditional targeted immunization into three kinds of immunization mechanisms on the di-rected network:the nodes that are immunized with large in-degrees;the nodes that are immunized with large out-degrees;the nodes that are immunized with both large in-degrees and large out-degrees.In the case where the node's infectivity function is a constant,we have proved that immunizing the nodes both large in-degrees and large out-degrees have the best effect,and the effect of immunizing nodes with large in-degrees is better than immu-nizing nodes with large out-degrees.Then we use numerical simulation to complement the results of our analysis.Two novel immunization strategies were proposed:combined immunization and du-plex immunization.Combined immunization is immunizing a neighbor node with large in-degree of susceptible node and immunizing a neighbor node with large out-degree of infected node at the same time.The duplex immunization divides the network into two parts by node's out-degree,and immunizes each part.We have shown that under the same average immunization rate,the effect of combined immunization is better than that of active immunization,and the effect of duplex immunization is better than that of active immuniza-tion,proportional immunization,acquaintance immunization,targeted immunization and combined immunization.