Reconstructing COVID-19 incidences from positive RT-PCR tests by deconvolution

The emergency of new COVID-19 variants over the past three years posed a serious challenge to the public health. Cities in China implemented mass daily RT-PCR tests by pooling strategies. However, a random delay exists between an infection and its first positive RT-PCR test. It is valuable for disease control to know the delay pattern and daily infection incidences reconstructed from RT-PCR test observations.

We formulated the convolution model between daily incidences and positive RT-PCR test counts as a linear inverse problem with positivity restrictions. Consequently, the Richard-Lucy deconvolution algorithm was used to reconstruct COVID-19 incidences from daily PCR tests. A real-time deconvolution was further developed based on the same mathematical principle. The method was applied to an Omicron epidemic data set of a bar outbreak in Beijing and another in Wuxi in June 2022. We estimated the delay function by maximizing likelihood via an E-M algorithm.

The delay function of the bar-outbreak in 2022 differs from that reported in 2020. Its mode was shortened to 4 days by one day. A 95% confidence interval of the mean delay is [4.43,5.55] as evaluated by bootstrap. In addition, the deconvolved infection incidences successfully detected two associated infection events after the bar was closed. The application of the real-time deconvolution to the Wuxi data identified all explosive incidence increases. The results revealed the progression of the two COVID-19 outbreaks and provided new insights for prevention and control strategies, especially for the role of mass daily RT-PCR testing.

The proposed deconvolution method is generally applicable to other infectious diseases if the delay model can be assumed to be approximately valid. To ensure a fair reconstruction of daily infection incidences, the delay function should be estimated in a similar context in terms of virus variant and test protocol. Both the delay estimate from the E-M algorithm and the incidences resulted from deconvolution are valuable for epidemic prevention and control. The real-time feedback is particularly useful during the epidemic's acute phase because it can help the local disease control authorities modify the control measures more promptly and precisely.