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Product adoption in heterogeneous networks: An epidemiological perspective

机译:异构网络中的产品采用:流行病学观点

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In this work, we use optimal control theory to characterize a variant of the viral marketing phenomenon over heterogeneous social networks. The marketing objective investigated in this framework is product adoption. In this context, we borrow concepts from the theory of epidemic processes to model the transitions of the members of the target market between different stages of the adoption process; specifically, we introduce a simple yet insightful 3-compartment setup, i.e., the potential-adopting-dormant-potential (PADoP) model, which is the equivalent of susceptible-infected-recovered-susceptible (SIRS) epidemic model. We then propose an optimal control scheme aiming at simultaneously optimizing the population of the adopting and dormant compartments under certain time and resource constraints. We prove the existence of the solution to the optimal control problem and provide both analytical and numerical solutions using Pontryagin Maximum Principle and forward-backward sweep method (FBSM), respectively. Simulations corroborate the findings of the paper.
机译:在这项工作中,我们使用最优控制理论来表征异构社交网络的病毒营销现象的变种。该框架调查的营销目标是产品采用。在这方面,我们借用流行病学理论的概念来模拟采用过程的不同阶段的目标市场成员的转型;具体而言,我们介绍了一个简单且富有洞察力的3个隔室设置,即潜在的 - 采用休眠 - 潜在(粉型)模型,这是相当于易受感染的恢复易感(SIRS)的流行病模型。然后,我们提出了一种最佳的控制方案,其旨在在某些时间和资源限制下同时优化采用和休眠隔室的群体。我们证明了对最佳控制问题的解决方案,并使用Pontryagin最大原理和前后扫描方法(FBSM)提供分析和数值解决方案。仿真证实了纸张的结果。

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