  The COVID-19 pandemic has posed significant challenges in modeling its
complex epidemic transmissions, infection and contagion, which are very
different from known epidemics. The challenges in quantifying COVID-19
complexities include effectively modeling its process and data uncertainties.
The uncertainties are embedded 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 apparent in the first two months of the COVID-19 pandemic, when the
relevant knowledge, case reporting and testing were all limited. Here we
introduce a novel hybrid approach Susceptible-Undocumented infected-Documented
infected-Recovered (SUDR) model. First, SUDR (1) characterizes and
distinguishes Undocumented (U) and Documented (D) infections commonly seen
during COVID-19 incubation periods and asymptomatic infections. Second, SUDR
characterizes the probabilistic density of infections by capturing exogenous
processes. Lastly, SUDR approximates 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 COVID-19 contagion, the
transmission rate is modeled by a time-varying density function of undocumented
infectious cases. By sampling from the mean-field posterior distribution with
reasonable priors, SUDR handles the randomness, noise and sparsity of COVID-19
observations widely seen in the public COVID-19 case data. The results
demonstrate a deeper quantitative understanding of the above uncertainties, in
comparison with classic SIR, time-dependent SIR, and probabilistic SIR models.
