A Mathematical Model of Social Media Popularity with Standard Incidence Rate

被引:1
作者
Windarto [1 ]
Purwati, Utami Dyah [1 ]
Amalia, Nadiyah [1 ]
机构
[1] Univ Airlangga, Fac Sci & Technol, Dept Math, Surabaya, Indonesia
来源
9TH ANNUAL BASIC SCIENCE INTERNATIONAL CONFERENCE 2019 (BASIC 2019) | 2019年 / 546卷
关键词
D O I
10.1088/1757-899X/546/5/052086
中图分类号
T [工业技术];
学科分类号
08 ;
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.
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页数:8
相关论文
共 13 条
[1]  
Anggriani N., 2015, Appl. Math. Sci., V9, P3775
[2]  
[Anonymous], 2014, ARXIV14014208
[3]  
[Anonymous], 2019, AVAILABLE GLOBAL SOC
[4]  
[Anonymous], 2011, MATH MODELS POPULATI
[5]   Is this the end for Facebook? A mathematical analysis [J].
DeLegge, Anthony ;
Wangler, Hannah .
APPLIED MATHEMATICS AND COMPUTATION, 2017, 305 :364-380
[6]  
Duggan Maeve, 2015, SOCIAL MEDIA UPDATE
[7]  
Gillete F, 2011, BLOOMBERG BUSINESSWE
[8]  
La Salle JP., 1976, The stability of dynamical systems, DOI [10.1137/1.9781611970432, DOI 10.1137/1.9781611970432]
[9]   College students' social networking experiences on Facebook [J].
Pempek, Tiffany A. ;
Yermolayeva, Yevdokiya A. ;
Calvert, Sandra L. .
JOURNAL OF APPLIED DEVELOPMENTAL PSYCHOLOGY, 2009, 30 (03) :227-238
[10]  
Phillips S., 2007, The Guardian