{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:27:17Z","timestamp":1760059637415,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T00:00:00Z","timestamp":1750982400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Informatics"],"abstract":"<jats:p>For the last decade, social networking services (SNS), such as X, Facebook, and Instagram, have become mainstream media for advertising and marketing. In SNS marketing, word-of-mouth among users can spread posted advertising information, which is known as viral marketing. In this study, we first analyzed the time series of user reactions to Instagram posts to clarify the characteristics of user behavior. Second, we modeled these variations using statistical distributions to predict the information diffusion of future posts and to provide some insights into the factors that affect users\u2019 reactions on Instagram using the estimated parameters of the modeling. Our results demonstrate that user reactions have a peak value immediately after posting and decrease drastically and exponentially as time elapses. In addition, modeling with the Weibull distribution is the most suitable for user reactions, and the estimated parameters help identify key factors that influence user reactions.<\/jats:p>","DOI":"10.3390\/informatics12030059","type":"journal-article","created":{"date-parts":[[2025,6,30]],"date-time":"2025-06-30T13:06:17Z","timestamp":1751288777000},"page":"59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigation of the Time Series Users\u2019 Reactions on Instagram and Its Statistical Modeling"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7291-0862","authenticated-orcid":false,"given":"Yasuhiro","family":"Sato","sequence":"first","affiliation":[{"name":"Graduate School of Engineering, Osaka Electro-Communication University, 18-8 Hatsucho, Neyagawa-shi 572-8530, Osaka, Japan"}]},{"given":"Yuhei","family":"Doka","sequence":"additional","affiliation":[{"name":"Graduate School of Engineering, Osaka Electro-Communication University, 18-8 Hatsucho, Neyagawa-shi 572-8530, Osaka, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,27]]},"reference":[{"key":"ref_1","unstructured":"CISCO (2023, May 15). Cisco Annual Internet Reposrt (2018\u20132023) White Paper. Available online: https:\/\/www.cisco.com\/."},{"key":"ref_2","unstructured":"DENTSU (2022, June 29). 2019 Advertising Expenditures in Japan. Available online: https:\/\/www.dentsu.com."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Luo, Z., Zhu, H., Zeng, D., and Yao, H. (2014, January 10\u201314). A Trace-Driven Analysis on the User Behaviors in Social E-Commerce Network. Proceedings of the 2014 IEEE International Conference on Communications (ICC), Sydney, Australia.","DOI":"10.1109\/ICC.2014.6883964"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"258","DOI":"10.2501\/jar-51-1-258-275","article-title":"Friends, Fans, and Followers: Do Ads Work on Social Networks?","volume":"51","author":"Taylor","year":"2011","journal-title":"J. Advert. Res."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yang, X., Kim, S., and Sun, Y. (2019, January 27\u201330). How Do Influencers Mention Brands in Social Media? Sponsorship Prediction of Instagram Posts. Proceedings of the 2019 IEEE\/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), Vancouver, BC, Canada.","DOI":"10.1145\/3341161.3342925"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Segev, N., Avigdor, N., and Avigdor, E. (2018, January 8\u201312). Measuring Influence on Instagram: A Network-Oblivious Approach. Proceedings of the 41st International ACM SIGIR Conference on Research & Development in Information Retrieval (SIGIR \u201918), Ann Arbor, MI, USA.","DOI":"10.1145\/3209978.3210134"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zarei, K., Ibosiola, D., Farahbakhsh, R., Gilani, Z., Garimella, K., Crespi, N., and Tyson, G. (2020, January 7\u201310). Characterising and Detecting Sponsored Influencer Posts on Instagram. Proceedings of the 2020 IEEE\/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), Hague, The Netherlands.","DOI":"10.1109\/ASONAM49781.2020.9381309"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"de Oliveira, L.M., and Goussevskaia, O. (2020, January 14\u201317). Topic Trends and User Engagement on Instagram. Proceedings of the 2020 IEEE\/WIC\/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology (WI-IAT), Melbourne, Australia.","DOI":"10.1109\/WIIAT50758.2020.00073"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hong, S.J., Ko, Y.Y., Joe, M., and Kim, S.W. (2019, January 8\u201312). Influence Maximization for Effective Advertisement in Social Networks: Problem, Solution, and Evaluation. Proceedings of the 34th ACM\/SIGAPP Symposium on Applied Computing (SAC), Limassol, Cyprus.","DOI":"10.1145\/3297280.3297412"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhan, Q., Yang, H., Wang, C., and Xie, J. (2013, January 4\u20136). CPP-SNS: A Solution to Influence Maximization Problem under Cost Control. Proceedings of the 2013 IEEE 25th International Conference on Tools with Artificial Intelligence, Herndon, VA, USA.","DOI":"10.1109\/ICTAI.2013.129"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Allaymoun, M.H., and Hamid, O.A.H. (2021, January 14\u201315). Business Intelligence Model to Analyze Social Network Advertising. Proceedings of the 2021 International Conference on Information Technology (ICIT), Amman, Jordan.","DOI":"10.1109\/ICIT52682.2021.9491635"},{"key":"ref_12","unstructured":"Hernandez-Bocanegra, D.C., Borchert, A., Br\u00fcnker, F., Shahi, G.K., and Ross, B. (2020, January 1\u20134). Towards a Better Understanding of Online Influence: Differences in Twitter Communication Between Companies and Influencers. Proceedings of the Australian Conference on Information Systems (ACIS 2020), Wellington, New Zealand."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1177\/14413582241247391","article-title":"Battle of Influence: Analysing the Impact of Brand-Directed and Influencer-Directed Social Media Marketing on Customer Engagement and Purchase Behaviour","volume":"33","author":"Kumar","year":"2024","journal-title":"Australas. Mark. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"056109","DOI":"10.1103\/PhysRevE.83.056109","article-title":"Social Network Dynamics of Face-to-Face Interactions","volume":"83","author":"Zhao","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s13278-022-00928-2","article-title":"Mining and Modelling Temporal Dynamics of Followers\u2019 Engagement on Online Social Networks","volume":"12","author":"Vassio","year":"2022","journal-title":"Soc. Netw. Anal. Min."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2700060","article-title":"Aggregate Characterization of User Behavior in Twitter and Analysis of the Retweet Graph","volume":"15","author":"Bild","year":"2015","journal-title":"ACM Trans. Internet Technol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Atienza-Barthelemy, J., Losada, J.C., and Benito, R.M. (2025). Modeling Information Diffusion on Social Media: The Role of the Saturation Effect. Mathematics, 13.","DOI":"10.3390\/math13060963"},{"key":"ref_18","unstructured":"(2021, October 15). Instagram Graph API. Available online: https:\/\/developers.facebook.com\/docs\/instagram-api."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0026-2714(92)90057-R","article-title":"A Least Square Estimation of Three Parameters of a Weibull Distribution","volume":"32","author":"Soman","year":"1992","journal-title":"Microelectron. 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