Mathematical Model of Social Media Popularity with Standard Incidence Rates

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The rapid development of science and technology provides positive benefits for human life, including ease of communication between individuals. Communication costs in the past are expensive. However, the current cost of communication is low due to the presence of various social media. Social media is an online application that allows users to post information about their profiles, including names, photos and other material for social media users to see. Furthermore, social media users can also communicate with each other in innovative ways.

One of the popular social media is Facebook. Facebook was launched in February 2004, by Mark Zuckerberg, a student at Harvard University. Facebook is a friendship site from the United States. It is estimated that 80% of internet users worldwide had a Facebook account in 2014, and 40% of them are active Facebook users or access Facebook once a year throughout the year. In October 2018, there were estimated 2.235 billion active Facebook users around the world. Facebook’s popularity reminds social media users to the popularity of the previous social media, Myspace. Myspace was launched in August 2003, but incomplete features on Myspace inspired Facebook to develop better features. Facebook has better features than Myspace, where Facebook offers a choice of customized profile pages, sharing photos, sharing music and online games. Incomplete features cause a rapid decline in the popularity of Myspace. As a result, NewsCrop, the owner of Myspace, sold Myspace. The rapid decline of Myspace can also occur on other social media such as Facebook.

Mathematical modeling has an important role in understanding many real problems, including the dynamics of social media users. The researchers built and analyzed many mathematical models to illustrate the dynamics of social media users. Cannarella and Spechler used epidemiological models such as SIR to describe user acceptance and user rejection of online social networks. From their model, Cannarella and Spechler predicted a rapid decline in Facebook activity in the years after 2014. Zhu et al. applying epidemic mathematical models to explain the adoption process and the process of leaving the media on the population of online social network users. From their model, Zhu et al. predicted demographic evolution in online social networking users. Tanaka et al. also applies epidemiological models such as SIR to explain the growth and decline of users of social networking services. Tanaka et al. found that the growth of users of social networking services can be accelerated by inviting new service users. Proskurnikov and Tempo discussed sustainable and discrete dynamic models to describe the dynamics of social networking. DeLegge and Wangler applied models like SIR to study the dynamics of Facebook users. DeLegge and Wangler found that Facebook hasn’t ended in 2017.

In their model, DeLegge and Wangler investigated the dynamics of vulnerable populations (populations of individuals currently not social media users, but open to joining as social media users), infected populations (populations of social media users) and populations that leave social media. DeLegge and Wangler used the incidence rate of bilinear to model the rate of increase in the population of social media users. Bilinear incidence rates are only accurate in the initial phase of the epidemic in a medium-sized population. Peulis has developed a mathematical model of DeLegge and Wangler by considering the incidence level of standard types. The model presented has three balance solutions (equilibrium points), the equilibrium point “without social media users”, the equilibrium point “social media is very popular” and the equilibrium point “popular social media”. The three equilibrium points are stable asymptotic sequences. The results of numerical simulations are consistent with the results of analytical studies of the model.

Author: Dr. Windarto, S.Sc., M.Sc. Faculty of Science and Technology, Universitas Airlangga Full article (open access) can be accessed via the page: https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052086

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