Modeling the dynamics of user adoption and abandonment for a single product

We introduce a compartmental differential equation model to study the dynamics of user adoption and abandonment for a single product. The model integrates two forms of abandonment: infectious, driven by user interactions, and non-infectious, prompted by external influences. Notably, the infectious abandonment coefficient varies linearly with the number of previous users. We investigate the existence of equilibria of the model and derive the threshold quantity ℛ0. The user-free equilibrium is always present, and its stability is analyzed under the condition ℛ0 < 1. Moreover, a user-prevailing equilibrium does not exist when ℛ0 ≤ 1, but at least one user-prevailing equilibrium is guaranteed when ℛ0 > 1. We further characterize conditions for multiple equilibria and various bifurcations, including saddle-node, 𝑆-shaped, and Hopf bifurcations, and formulate an optimal control problem. Numerical simulations validate our theoretical findings, and the historical LinkedIn and YouTube data calibrate the model to forecast future user adoption trends.

Grantor dc:publisher

University of Tennessee at Chattanooga

Year dc:date.available

2026

Author dc:creator

• Nguyen, Uyen

Contributors dc:contributor

• Kong, Lingju
• Wang, Xiunan; Wang, Jin; Graef, John R.
• College of Arts and Sciences

• Bifurcation theory
• Consumer behavior--Mathematical models
• Differential equations
• Diffusion of innovations--Mathematical models
• Nonlinear systems
• Pontryagin spaces
• Product life cycle--Mathematical models

Licence

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/997

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-2164