Modeling And Study Of Three Kinds Of Propagation Phenomena

Propagation is a common phenomenon in nature,human society and engineering technology.An important mission of human beings is to understand the law of propagation and exploit it to benefit ourselves.After experiencing the long agricultural era and the relatively long industrial era,human beings finally entered the landmark information era in the middle of the twentieth Century.Propagation of information can not live without network.In order to understand the key factors that influence information dissemination and then put forward a strategy of containment / promotion,a new subject named network propagating dynamics was born.The propagating dynamics of network is aimed at establishing dynamical models capturing the propagating rules of information by taking into full account various factors,especially countermeasures,that have significant impact on the spread of virus,understanding the propagating laws of information and evaluating the cost and effectiveness of different virus-containing policies through in-depth model analysis;thereby presenting a feasible set of cost-effective information-containing/promoting policies.This thesis is devoted to the understanding of propagating laws of information and the evaluation of information-containing/promoting policies.The major contributions are listed as follows.·Alerting at the early stage of malware invasion turns out to be an important complement to malware detection and elimination.This section addresses the issue of how to dynamically contain the prevalence of malware at a lower cost,provided alerting is feasible.A controlled epidemic model with alert is established,and an optimal control problem based on the epidemic model is formulated.The optimality system for the optimal control problem is derived.The structure of an optimal control for the proposed optimal control problem is characterized under some conditions.Numerical examples show that the cost-efficiency of an optimal control strategy can be enhanced by adjusting the upper and lower bounds on admissible controls.·As a new type of cyber-attacks,advanced persistent threats(APTs)pose a severe threat to modern society.This paper focuses on the assessment of the risk of APTs.Based on a dynamic model characterizing the time evolution of the state of an organization,the organization's risk is defined as its maximum possible expected loss,and the risk assessment problem is modeled as a constrained optimization problem.The influence of different factors on an organization's risk is uncovered through theoretical analysis.Based on extensive experiments,we speculate that the attack strategy obtained by applying the hill-climbing method to the proposed optimization problem,which we call the HC strategy,always leads to the maximum possible expected loss.We then present a set of five heuristic attack strategies and,through comparative experiments,show that the HC strategy causes a higher risk than all these heuristic strategies do,which supports our conjecture.Finally,the impact of two factors on the attacker's HC cost profit is determined through computer simulations.These findings help understand the risk of APTs in a quantitative manner.·This section addresses the discount pricing in word-of-mouth(WOM)marketing.A new discount strategy known as the Infection-Based Discount(IBD)strategy is proposed.The basic idea of the IBD strategy lies in that each customer enjoys a discount that is linearly proportional to his/her influence in the WOM network.To evaluate the performance of the IBD strategy,the WOM spreading process is modeled as a dynamic model known as the DPA model,and the performance of the IBD strategy is modeled as a function of the basic discount.Next,the influence of different factors,including the basic discount and the WOM network,on the dynamics of the DPA model is revealed experimentally.Finally,the influence of different factors on the performance of the IBD strategy is uncovered experimentally.On this basis,some promotional measures are recommended.