Locally Adaptive Integrated Brownian Motion for Epidemic Growth Rate Inference

Music City Center 

During an infectious disease outbreak, the growth rate (r) quantifies the relative change in cases over time. Integrated Brownian Motion (IBM)—the time integral of a Wiener process—can be modeled as a Markov process when modeled jointly with its derivative, which allows for a state space representation and therefore avoids potentially costly matrix inversions. This makes IBM a computationally efficient smoothing prior when the derivative (i.e., the growth rate) is of primary interest. Real-world case trajectories, however, often exhibit both gradual trends and abrupt shifts, like sudden surges driven by emerging variants or waning immunity. Standard Gaussian priors do not capture these mixed dynamics effectively, as they can either oversmooth rapid changes or produce overly noisy estimates during stable periods. To address this, we propose a locally adaptive extension of IBM that can flexibly model both gradual and abrupt changes in case incidence. We demonstrate the effectiveness of this method using simulated outbreak data and California county-level SARS-CoV-2 data.