  Extreme public health interventions play a critical role in mitigating the
local and global prevalence and pandemic potential of COVID-19. Here, we use
population size for pathogen transmission to measure the intensity of public
health interventions, which is a key characteristic variable for nowcasting and
forecasting of the epidemic. By formulating a hidden Markov dynamic system and
using nonlinear filtering theory, we have developed a stochastic epidemic
dynamic model under public health interventions. The model parameters and
states are estimated in time from internationally available public data by
combining an unscented filter and an interacting multiple model filter.
Moreover, we consider the computability of the population size and provide its
selection criterion. We estimate the mean of the basic reproductive number of
China and the rest of the globe except China (GEC) to be 2.46 (95% CI:
2.41-2.51) and 3.64 (95% CI: (3.55-3.72), respectively. We infer that the
number of latent infections of GEC is about 7.47*10^5 (95% CI:
7.32*10^5-7.62*10^5) as of April 2, 2020. We predict that the peak of
infections in hospitals of GEC may reach 3.00*10^6 on the present trajectory,
i.e., if the population size for pathogen transmission and epidemic parameters
remains unchanged. If the control intensity is strengthened, e.g., 50%
reduction or 75% reduction of the population size for pathogen transmission,
the peak would decline to 1.84*10^6, 1.27*10^6, respectively.
