Maximum profit of viral marketing: an optimal control approach

© 2019 Association for Computing Machinery. Viral marketing, known also as word-of-mouth marketing, is to use consumer-to-consumer communications to disseminate information about a product or service. Firms must persuade consumers, through their personal network and with the support of the Internet to become the vehicles which can disseminate the positive information. This paper addresses the modeling and analysis of the viral marketing for a consistent set of items. We develop a node-level positive comments mixed spreading model with positive comments and discount pricing mechanism, and thereby we measure the profit of the marketing. Next, we show that the model admits an optimal control, and we present the optimality system for solving the model. Finally, we give some optimal strategies by solving the corresponding optimality systems.