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).
Highlights
In our analysis we only consider the states for which daily observations on Ct, Dt, Rtreported, Qt, and Ht are available throughout the time window under consideration
We present results for fifteen states in the United States (US) that demonstrate the efficacy of the proposed model and the estimation methods
We present a summary of the results obtained from applications of the proposed method on the data procured from fifteen other states in the US
Summary
Such models yield estimates of epidemiological markers such as the basic reproduction number ( R0 ), and various doubling and case fatality rates that are indicators of the disease growth pattern[27,28]. Since the number of infected but asymptomatic individuals is unknown, conventional epidemiological models of disease spread do not readily apply to the COVID-19 dynamics.
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