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Abstract The evolution of the COVID-19 pandemic is described through a time-dependent stochastic dynamic model in discrete time. The proposed multi-compartment model is expressed through a system of difference equations. Information on the social distancing measures and diagnostic testing rates are incorporated to characterize the dynamics of the various compartments of the model. In contrast with conventional epidemiological models, the proposed model involves interpretable temporally static and dynamic epidemiological rate parameters. A model fitting strategy built upon nonparametric smoothing is employed for estimating the time-varying parameters, while profiling over the time-independent parameters. Confidence bands of the parameters are obtained through a residual bootstrap procedure. A key feature of the methodology is its ability to estimate latent unobservable compartments such as the number of asymptomatic but infected individuals who are known to be the key vectors of COVID-19 spread. The nature of the disease dynamics is further quantified by relevant epidemiological markers that make use of the estimates of latent compartments. The methodology is applied to understand the true extent and dynamics of the pandemic in various states within the United States (US). 

Making statistical inference on quantities defining various characteristics of a temporally measured biochemical process and analyzing its variability across different experimental conditions is a core challenge in various branches of science. This problem is particularly difficult when the amount of data that can be collected is limited in terms of both the number of replicates and the number of time points per process trajectory. We propose a method for analyzing the variability of smooth functionals of the growth or production trajectories associated with such processes across different experimental conditions. Our modeling approach is based on a spline representation of the mean trajectories. We also develop a bootstrap-based inference procedure for the parameters while accounting for possible multiple comparisons. This methodology is applied to study two types of quantities—the “time to harvest” and “maximal productivity”—in the context of an experiment on the production of recombinant proteins. We complement the findings with extensive numerical experiments comparing the effectiveness of different types of bootstrap procedures for various tests of hypotheses. These numerical experiments convincingly demonstrate that the proposed method yields reliable inference on complex characteristics of the processes even in a data-limited environment where more traditional methods for statistical inference are typically not reliable.