Tracking the transmission dynamics of COVID‐19 with a time‐varying coefficient state‐space model

Abstract

The spread of COVID‐19 has been greatly impacted by regulatory policies and behavior patterns that vary across counties, states, and countries. Population‐level dynamics of COVID‐19 can generally be described using a set of ordinary differential equations, but these deterministic equations are insufficient for modeling the observed case rates, which can vary due to local testing and case reporting policies and nonhomogeneous behavior among individuals. To assess the impact of population mobility on the spread of COVID‐19, we have developed a novel Bayesian time‐varying coefficient state‐space model for infectious disease transmission. The foundation of this model is a time‐varying coefficient compartment model to recapitulate the dynamics among susceptible, exposed, undetected infectious, detected infectious, undetected removed, hospitalized, detected recovered, and detected deceased individuals. The infectiousness and detection parameters are modeled to vary by time, and the infectiousness component in the model incorporates information on multiple sources of population mobility. Along with this compartment model, a multiplicative process model is introduced to allow for deviation from the deterministic dynamics. We apply this model to observed COVID‐19 cases and deaths in several U.S. states and Colorado counties. We find that population mobility measures are highly correlated with transmission rates and can explain complicated temporal variation in infectiousness in these regions. Additionally, the inferred connections between mobility and epidemiological parameters, varying across locations, have revealed the heterogeneous effects of different policies on the dynamics of COVID‐19.

Inference under superspreading: Determinants of SARS‐CoV‐2 transmission in Germany

“…The presented model is based on overdispersion in individual transmission and deviates from the literature, where overdispersion is often ignored 11,32‐36 or assumed to be constant for aggregated infections, 14,37 that is, $$$ {i}_t\sim \mathrm{NB}\left({i}_{t-1}{R}_t,\Psi \right) $$$. This alternative assumption of a constant dispersion is inherent, but often unappreciated, in inference based on standard negative binomial regression, the endemic/epidemic model, 38,39 and epidemiological models with random effects 40 .…”

“…The presented model is based on overdispersion in individual transmission and deviates from the literature, where overdispersion is often ignored 11,[32][33][34][35][36] or assumed to be constant for aggregated infections, 14,37 that is,…”

Explaining Transmission Rate Variations and Forecasting Epidemic Spread in Multiple Regions with a Semiparametric Mixed Effects SIR Model

“…Similar limitations are present in Johndrow et al (2020) and others who model transmission rate as a piecewise function. Keller et al (2022) developed a sophisticated methodology for estimating covariate effects with a smooth temporal deviation and a multiplicative process for state-evolution error.…”

“…Zhou and Ji (2020) fitted a latent Gaussian process (GP) model using a Parallel Tempering MCMC algorithm (Woodard et al, 2009;Miasojedow et al, 2013), but did not incorporate a hierarchy to borrow information across parallel streams of incidence data, and reported challenges with covariate effect estimation. Keller et al (2022) invoked HMC sampling algorithms implemented via Stan (Carpenter et al, 2017).…”

“…Keller et al. (2022) developed a sophisticated methodology for estimating covariate effects with a smooth temporal deviation and a multiplicative process for state‐evolution error.…”