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

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 2 months of the COVID-19 pandemic, when the relevant knowledge, case reporting and testing were all limited. Here we introduce a novel hybrid approach SUDR by expanding the foundational compartmental epidemic Susceptible-Infected-Recovered (SIR) model with two compartments to a 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 like clustering contagion interactions, superspreading, and social reinforcement. 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.