Abstract
1- Introduction
2- Proposed model and mean-field analysis
3- Graph-theoretical analysis
4- Numerical results
5- Conclusion
References
Abstract
Omnipresent online social media nowadays has a constantly growing influence on business, politics, and society. Understanding these newer mechanisms of information diffusion is very important for deciding campaign policies. Due to free interaction among a large number of members, information diffusion on social media has various characteristics similar to an epidemic. In this paper, we propose and analyze a mathematical model to understand the phenomena of digital marketing with an epidemiological approach considering some realistic interactions in a social network. We apply mean-field approach as well as network analysis to investigate the phenomenon for both homogeneous and heterogeneous models, and study the diffusion dynamics as well as equilibrium states for both the cases. We explore the parameter space and design strategies to run an advertisement campaign with substantial efficiency. Moreover, we observe the phenomena of bistability, following which we estimate the necessary conditions to make a campaign more sustainable while ensuring its viral spread.
Introduction
In this age of the Internet, the importance of social networks to spread a message, opinion or campaign is undeniable [1, 2, 3]. Devising strategies to exploit existing social networks to make a campaign fast spreading as well as sustainable is becoming an area of growing interest among political campaigners and product marketing managers. Based on this ideas, viral marketing (VM) is being adopted as a recent marketing strategy and a way of communication with customers, which can potentially reach a large audience very fast [4, 5, 6]. VM is also known as Internet Word-of-mouth marketing, as it encourages people to share information (product specifications, improvements, campaigns etc.) with their friends through email or other social media, and utilizes existing social networks [7]. This prompting is sometimes done by introduction of some benefits (like, credit points, e-cash, extra discounts, cashback, promo codes etc.) to the existing customers, as a reward for sharing information in their peer network. VM campaigns have several benefits over traditional mass media campaigns, an important one being its ability to reach particular customer groups, as, in many cases, friendship networks arise from common interests [8]. These communications also have more impact and acceptability than third-party advertising among the potential customers, as it comes with an endorsement and recommendation of a friend. Woerdl [9] has also highlighted fast and exponential diffusion among the audience and voluntary transmission by sender as some of the important benefits of viral marketing. The dynamics of VM campaign spread are much similar to that of infectious disease, as they have a contagious quality, being beneficial for the existing consumers and propagating via social interaction. Prominent companies like Amazon, Google and Hotmail have succeeded with virtually no marketing, based solely on consumer-driven communications [10].