Estimating the instantaneous reproduction number ($R_t$) by using particle filter

Background: Monitoring the transmission of coronavirus disease 2019 (COVID-19) requires accurate estimation of the effective reproduction number ($R_t$). However, existing methods for calculating $R_t$ may yield biased estimates if important real-world factors, such as delays in confirmation, pre-symptomatic transmissions, or imperfect data observation, are not considered.

Method: To include real-world factors, we expanded the susceptible-exposed-infectious-recovered (SEIR) model by incorporating pre-symptomatic (P) and asymptomatic (A) states, creating the SEPIAR model. By utilizing both stochastic and deterministic versions of the model, and incorporating predetermined time series of $R_t$, we generated simulated datasets that simulate real-world challenges in estimating $R_t$. We then compared the performance of our proposed particle filtering method for estimating $R_t$ with the existing EpiEstim approach based on renewal equations.

Results: The particle filtering method accurately estimated $R_t$ even in the presence of data with delays, pre-symptomatic transmission, and imperfect observation. When evaluating via the root mean square error (RMSE) metric, the performance of the particle filtering method was better in general and was comparable to the EpiEstim approach if perfectly deconvolved infection time series were provided, and substantially better when $R_t$ exhibited short-term fluctuations and the data was right truncated.

Conclusions: The SEPIAR model, in conjunction with the particle filtering method, offers a reliable tool for predicting the transmission trend of COVID-19 and assessing the impact of intervention strategies. This approach enables enhanced monitoring of COVID-19 transmission and can inform public health policies aimed at controlling the spread of the disease.