The novel coronavirus disease 2019 (COVID-19) presents unique and unknown problem complexities and modeling challenges, where an imperative task is to model both its process and data uncertainties, represented in implicit and high-proportional undocumented infections, asymptomatic contagion, social reinforcement of infections, and various quality issues in the reported data. These uncertainties become even more phenomenal in the overwhelming mutation-dominated resurgences with vaccinated but still susceptible populations. Here we introduce a novel hybrid approach to (1) characterizing and distinguishing Undocumented (U) and Documented (D) infections commonly seen during COVID-19 incubation periods and asymptomatic infections by expanding the foundational compartmental epidemic Susceptible-Infected-Recovered (SIR) model with two compartments, resulting in a new Susceptible-Undocumented infected-Documented infected-Recovered (SUDR) model; (2) characterizing the probabilistic density of infections by empowering SUDR to capture exogenous processes like clustering contagion interactions, superspreading and social reinforcement; and (3) approximating the density likelihood of COVID-19 prevalence over time by incorporating Bayesian inference into SUDR. Different from existing COVID-19 models, SUDR characterizes the undocumented infections during unknown transmission processes. To capture the uncertainties of temporal transmission and social reinforcement during the COVID-19 contagion, the transmission rate is modeled by a time-varying density function of undocumented infectious cases. We solve the modeling by sampling from the mean-field posterior distribution with reasonable priors, making SUDR suitable to handle the randomness, noise and sparsity of COVID-19 observations widely seen in the public COVID-19 case data.
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