The UTC Graduate School is pleased to announce that Uyen Nguyen will present Master’s research titled, Modeling the Dynamics of User Adoption and Abandonment for a Single Product on 02\/28\/2025 at 2:00 PM in Lupton 392. Everyone is invited to attend.
Mathematics
Chair: Lingju Kong
Co-Chair:
Abstract:
We present a new compartmental differential equation model to explore the dynamics of user adoption and abandonment for a single product. Our model incorporates two distinct types of abandonment: infectious abandonment, driven by interactions among current and former users, and non-infectious abandonment, triggered by factors such as mass media, advertisements, or the introduction of new products. Unlike previous studies, we treat the infectious abandonment coefficient as a variable that changes linearly with the number of previous users, rather than as a constant. This introduces additional complexity to the model while also enriching its dynamic behavior. We investigate the existence of equilibria in 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. Furthermore, we show that a user-prevailing equilibrium does not exist when R0 = 1, but at least one user-prevailing equilibrium is guaranteed when R0 > 1. We determine the criteria for the existence of one, two, or three user-prevailing equilibria and establish the conditions under which S-shaped and saddle-node bifurcations can arise. Additionally, we establish criteria for different types of Hopf bifurcations. We also explore an optimal control problem related to the model, identifying the system that must be satisfied by the optimal control pair. Our theoretical results are further validated through extensive numerical simulations. To demonstrate the practical applicability of our model, we calibrate it using historical data on LinkedIn registered users. The calibrated model is then employed to provide forecasts for future user adoption trends.<\/p>\n","protected":false},"excerpt":{"rendered":"
The UTC Graduate School is pleased to announce that Uyen Nguyen will present Master’s research titled, Modeling the Dynamics of User Adoption and Abandonment for a Single Product on 02\/28\/2025 at 2:00 PM in Lupton 392. Everyone is invited to attend. Mathematics Chair: Lingju Kong Co-Chair: Abstract: We present a new compartmental differential equation model to explore the dynamics of user… <\/p>\n