Dynamical Analysis of Online Shopping with Beauty Influencer

Meri Teri Andani; Zulaikha Zulaikha

doi:10.37905/jjom.v7i2.33363

Dynamical Analysis of Online Shopping with Beauty Influencer

Meri Teri Andani, Zulaikha Zulaikha

Abstract

This study develops a modified nonlinear mathematical model of online shopping dynamics that explicitly incorporates the direct influence of beauty influencers through promotional content (F) and a parameter α for transition from offline to online shopping without the influence of influencers. The model comprises offline shoppers (L), online shoppers (O), and the amount of promotional content created by beauty influencers (F). Stability analysis shows two equilibrium points: an online shopping-free state E1 locally asymptotically stable when R0 < 1 and an endemic state E2 locally asymptotically stable when R0 > 1. Numerical simulations using MATLAB R2013a confirm the analysis, revealing that higher promotional content growth rates (k) and lower decline rates (θ) increase R0 and the online shoppers population. The novelty lies in explicitly modeling influencer-based promotional content as a driver of shopping behavior, offering strategic insights for sustained engagement and customer retention in beauty sector digital marketing.

Keywords

Dynamic system; Stability analysis; Online shopping; Influencer

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References

S. Sharma, “Modelling the role of information on the spread of online shopping,” Computational and Mathematical Methods, vol. 3, no. 4, p. e1182, 2021, doi: 10.1002/cmm4.1182.

Capital One Shopping, “Total number of online stores,” 2024, [Online]. Available: https://capitaloneshopping.com/research/number-of-online-stores/

. [Accessed: 02-Sep-2024].

Y. Rianto, R. Lumanto, and S. Meiningsing, Potret Belanja Online di Indonesia. Jakarta Pusat: Pusat Data dan Sarana Informatika, 2013.

Asosiasi Penyelenggara Jasa Internet Indonesia (APJII), “Jumlah pengguna internet Indonesia tembus 221 juta orang,” 2024, [Online]. Available: https://apjii.or.id/berita/d/apjii-jumlah-pengguna-internet-indonesia-tembus-221-juta-orang

. [Accessed: 02-Sep-2024].

Statista, “Share of people who have purchased an item or product because it was endorsed by an influencer in Indonesia as of May 2023,” 2024, [Online]. Available: https://www.statista.com/statistics/1201127/indonesia-influencer-impact-on-buyer-behavior/

. [Accessed: 02-Sep-2024].

D. Vrontis, A. Makrides, M. Christofi, and A. Giordano, “Social media influencer marketing: A systematic review, integrative framework and future research agenda,” International Journal of Consumer Studies, vol. 45, no. 4, pp. 617–644, 2021, doi: 10.1111/ijcs.12647.

Influencer Marketing Hub, “Influencer marketing benchmark report 2023,” 2023, [Online]. Available: https://influencermarketinghub.com/ebooks/InfluencerMarketingBenchmarkReport2023.pdf

. [Accessed: 02-Sep-2024].

M. K. D. Purnamasari, A. Fitriyah, and Zulaikha, “Mathematical modelling of the spread of COVID-19 with first, second and third doses of vaccination in Semarang City,” Journal of Fundamental Mathematics and Applications, vol. 7, no. 1, 2024, doi: 10.14710/jfma.v7i1.19750.

M. Hermann and M. Saravi, Nonlinear Ordinary Differential Equations: Analytical Approximation and Numerical Methods. Springer, 2016.

A. K. Misra, K. Goyal, and J. Maurya, “Impact of social media advertisements on the dynamics of online shopping: A modeling study,” Differential Equations and Dynamical Systems, vol. 31, no. 3, pp. 651–671, 2022, doi: 10.1007/s12591-022-00598-8.

S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed. Springer, 2003.

R. N. Shadrina and Y. Sulistyanto, “Analisis pengaruh content marketing, influencer, dan media sosial terhadap keputusan pembelian konsumen (studi pada pengguna Instagram dan TikTok di Kota Magelang),” Diponegoro Journal of Management, vol. 11, no. 1, pp. 1–10, 2022.

F. Frahyanti, M. A. Syafi’i, and H. S. Devi, “Analisis faktor-faktor yang menyebabkan konsumen memilih belanja online store daripada offline store,” Sahmiyya: Jurnal Ekonomi dan Bisnis, vol. 3, no. 1, pp. 42–49, 2024.

A. Afika, P. O. D. Yulian, and I. Pasulu, “Pengaruh online shop terhadap minat beli barang secara online pada mahasiswa Fakultas Ekonomi Universitas Kristen Indonesia Toraja,” in Prosiding Seminar Nasional Manajemen dan Ekonomi, 2023, pp. 257–265.

Digital Marketing Institute, “20 surprising influencer marketing statistics,” 2024, [Online]. Available: https://digitalmarketinginstitute.com/blog/20-influencer-marketing-statistics-that-will-surprise-you

. [Accessed: 06-Feb-2025].

Febby, “Influencer fatigue,” 2025, [Online]. Available: https://kol.id/blog/influencer-fatigue

. [Accessed: 06-Feb-2025].

Bithour Production, “Kekurangan influencer marketing,” 2023, [Online]. Available: https://bithourproduction.com/blog/kekurangan-influencer-marketing/

. [Accessed: 06-Feb-2025].

A. Lamis, “Analisis dinamik model penyebaran rumor dengan kontrol optimal pada penyebaran berita di media,” Skripsi, Universitas Brawijaya, Malang, 2019.

J. Maurya, K. Goyal, and A. K. Misra, “Modeling the impact of social media on the adoption of a new product by customers,” MethodsX, vol. 9, p. 101932, 2022, doi: 10.1016/j.mex.2022.101932.

F. Brauer, P. van den Driessche, and J. Wu, Eds., Mathematical Epidemiology. Berlin, Heidelberg: Springer, 2008, vol. 1945.

Q. Liu, “How beauty influencers on TikTok can affect the purchasing of cosmetics,” SHS Web of Conferences, vol. 165, p. 02022, 2023, doi: 10.1051/shsconf/202316502022.

D. N. Lailia and R. Andriana, “Pengaruh promosi online dan harga terhadap minat beli serta dampaknya pada keputusan pembelian belanja online di Shopee,” in Prosiding Seminar Nasional Forum Manajemen Indonesia, vol. 1, 2023, doi: 10.47747/snfmi.v1i.1551.

A. Yoebrilianti, “Pengaruh promosi penjualan terhadap minat beli produk fashion dengan gaya hidup sebagai variabel moderator (survei konsumen pada jejaring sosial),” Jurnal Manajemen, vol. 8, no. 1, pp. 20–30, 2014.

DOI: https://doi.org/10.37905/jjom.v7i2.33363