Hybrid SIS Dynamics for Demand Modeling of Frequently Updated Products

We propose a hybrid spreading process model to capture the dynamics of demand for software-based products. We introduce discontinuous jumps in the state to model sudden surges in demand that can be seen immediately after a product update is released. After each update, the modeled demand evolves according to a continuous-time susceptible-infected-susceptible (SIS) epidemic model. We identify the necessary and sufficient conditions for estimating the hybrid model's parameters for an arbitrary finite number of sequential updates. We verify the parameter estimation conditions in simulation, and evaluate how the estimation of these parameters is impacted by the presence of observation and process noise. We then validate our model by applying our estimation method to daily user engagement data for a regularly updating software product, the live-service video game `Apex Legends.'