A Mathematical Model of Social Media Popularity with Standard Incidence Rate

9th Annual Basic Science International Conference 2019

自然科学（总论）

Windarto^1 ; Purwati, Utami Dyah^1 ; Amalia, Nadiyah^1

Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Indonesia^1

关键词: Analytical results;    Asymptotically stable;    Bilinear incidence rates;    Facebook;    Social media;    Standard incidence rate;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052086/pdf
DOI  :  10.1088/1757-899X/546/5/052086

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

Facebook, Instagram, Twitter are some popular social media. DeLegge and Wangler (2017) have developed a Susceptible-Infectious-Removed type mathematical model to describe social media popularity. The DeLegge and Wangler model was a bilinear incidence rate model. In this paper, we improve the DeLegge and Wangler model by considering standard incidence rate. The presented model takes the form of an ordinary differential equation system that describes dynamic of susceptible (population of who are not social media users), infectious population (population of social networks users) and removed population (population of who leave social media). The presented model has three equilibria namely the "no social media users" equilibrium, "very popular social media" equilibrium and "popular social media" equilibrium. We find that the three equilibria are conditionally asymptotically stable. We also perform some numerical simulations to verify the analytical results.