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The COVID-19 pandemic has posed significant challenges in modeling itscomplex epidemic transmissions, infection and contagion, which are verydifferent from known epidemics. The challenges in quantifying COVID-19complexities include effectively modeling its process and data uncertainties.The uncertainties are embedded in implicit and high-proportional undocumentedinfections, asymptomatic contagion, social reinforcement of infections, andvarious quality issues in the reported data. These uncertainties become evenmore apparent in the first two months of the COVID-19 pandemic, when therelevant knowledge, case reporting and testing were all limited. Here weintroduce a novel hybrid approach Susceptible-Undocumented infected-Documentedinfected-Recovered (SUDR) model. First, SUDR (1) characterizes anddistinguishes Undocumented (U) and Documented (D) infections commonly seenduring COVID-19 incubation periods and asymptomatic infections. Second, SUDRcharacterizes the probabilistic density of infections by capturing exogenousprocesses. Lastly, SUDR approximates the density likelihood of COVID-19prevalence over time by incorporating Bayesian inference into SUDR. Differentfrom existing COVID-19 models, SUDR characterizes the undocumented infectionsduring unknown transmission processes. To capture the uncertainties of temporaltransmission and social reinforcement during COVID-19 contagion, thetransmission rate is modeled by a time-varying density function of undocumentedinfectious cases. By sampling from the mean-field posterior distribution withreasonable priors, SUDR handles the randomness, noise and sparsity of COVID-19observations widely seen in the public COVID-19 case data. The resultsdemonstrate a deeper quantitative understanding of the above uncertainties, incomparison with classic SIR, time-dependent SIR, and probabilistic SIR models.

Modeling time evolving COVID-19 uncertainties with density dependent asymptomatic infections and social reinforcement