Estimation of local time-varying reproduction numbers in noisy surveillance data

Abstract

A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia.

Fig 1.

Schematic of our method to account for misidentification. Note that we do not back-calculate $I_{*}^{\text{local}}(t)$ and $I_{*}^{\text{imported}}(t)$ from estimated I^local(t) and I^imported(t) in this paper.

Fig 2.

The means of daily local and imported diagnosed counts in 1,000 simulation trials for epidemics in Hong Kong and Victoria.

Fig 3.

Estimations of local time-varying reproduction numbers in simulated epidemics for Hong Kong and Victoria under three sets of error misidentification rates: α₀ ~ 0.1, and α₁ ~ 0.3, 0.4, or 0.5. The error bands are the averages of 95% credible intervals over 1,000 trials at each time point.

Fig 4.

Estimations of local time-varying reproduction numbers in simulated epidemics for Hong Kong and Victoria under three sets of error misidentification rates: α₁ ~ 0.1, and α₀ ~ 0.3, 0.4, or 0.5. The error bands are the averages of 95% credible intervals over 1,000 trials at each time point.

Fig 5.

Epidemic curves of COVID-19 cases and estimations of local time-varying reproduction numbers in Hong Kong and Victoria. (a) The epidemic curve of daily cases of laboratory-confirmed SARS-CoV-2 infection in Hong Kong by symptom onset date and colored by case category. Asymptomatic cases are included here by date of confirmation. (b) The epidemic curve of the coronavirus disease cases in Victoria by sample collection date and colored by case category. (c) and (d) Estimations of local time-varying reproduction numbers under three assumed scenarios: 1) no identification error, 2) α₀ ~ 0.1 and α₁ ~ 0.3 (around 10% imported cases are misclassified as local and around 30% local cases are misclassified as imported), 3) α₀ ~ 0.3 and α₁ ~ 0.1 (around 30% imported cases are misclassified as local and around 10% local cases are misclassified as imported). The bands are the 95% credible intervals.