Using the contact network model and Metropolis-Hastings sampling to reconstruct the COVID-19 spread on the "Diamond Princess"

Abstract

Traditional compartmental models such as SIR (susceptible, infected, recovered) assume that the epidemic transmits in a homogeneous population, but the real contact patterns in epidemics are heterogeneous. Employing a more realistic model that considers heterogeneous contact is consequently necessary. Here, we use a contact network to reconstruct unprotected, protected contact, and airborne spread to simulate the two-stages outbreak of COVID-19 (coronavirus disease 2019) on the "Diamond Princess" cruise ship. We employ Bayesian inference and Metropolis-Hastings sampling to estimate the model parameters and quantify the uncertainties by the ensemble simulation technique. During the early epidemic with intensive social contacts, the results reveal that the average transmissibility $t$ was 0.026 and the basic reproductive number $R_0$ was 6.94, triple that in the WHO report, indicating that all people would be infected in one month. The $t$ and $R_0$ decreased to 0.0007 and 0.2 when quarantine was implemented. The reconstruction suggests that diluting the airborne virus concentration in closed settings is useful in addition to isolation, and high-risk susceptible should follow rigorous prevention measures in case exposed. This study can provide useful implications for control and prevention measures for the other cruise ships and closed settings.

Keywords: Airborne spread; Chain-binomial model; Contact network model; Small-world; The basic reproductive number R0; Transmissibility.

Fig. 1

The daily confirmed cases and two stages (1, 2a and 2b) in the “Diamond Princess” epidemic.

Fig. 2

Brief depiction of the contact network, where white, black and aquamarine nodes present infected, susceptible and isolated individuals, respectively. The dashed red edges represent the changed edges.

Fig. 3

The flow diagram of chain-binomial model, where $G(t)$ obeys the geometric distribution with the probability of success $t$ and the maximum times that the Bernoulli trial can be implemented, $r$ is a random sampling of $G\left(t\right).$

Fig. 4

Flowchart of parameter perturbation and ensemble simulation for epidemic models.

Fig. 5

Histograms of samples from the parameters’ posterior distributions for epidemic models on the “Diamond Princess”. The vertical dashed lines indicate the modes of samples, which can be regarded as the selected parameters, i.e., (9.76, 0.41, 0.026) for stage 1 (the first row), (12.43, 0.16, 0.0007) for stage 2a (the second row) and 9.63 × 10⁻⁸ for stage 2b (the third row).

Fig. 6

The daily epidemic curves on the “Diamond Princess”. The reference is the final number of infected staying on the ship. (a) Epidemic curves without any quarantine from 20 January to 19 February 2020; (b) stage 1; (c) stage 2a; (d) stage 2b.