Transmission dynamics informed neural network with application to COVID-19 infections.

Since the end of 2019 the COVID-19 repeatedly surges with most countries/territories experiencing multiple waves, and mechanism-based epidemic models played important roles in understanding the transmission mechanism of multiple epidemic waves. However, capturing temporal changes of the transmissibility of COVID-19 during the multiple waves keeps ill-posed problem for traditional mechanism-based epidemic compartment models, because that the transmission rate is usually assumed to be specific piecewise functions and more parameters are added to the model once multiple epidemic waves involved, which poses a huge challenge to parameter estimation. Meanwhile, data-driven deep neural networks fail to discover the driving factors of repeated outbreaks and lack interpretability. In this study, aiming at developing a data-driven method to project time-dependent parameters but also merging the advantage of mechanism-based models, we propose a transmission dynamics informed neural network (TDINN) by encoding the SEIRD compartment model into deep neural networks. We show that the proposed TDINN algorithm performs very well when fitting the COVID-19 epidemic data with multiple waves, where the epidemics in the United States, Italy, South Africa, and Kenya, and several outbreaks the Omicron variant in China are taken as examples. In addition, the numerical simulation shows that the trained TDINN can also perform as a predictive model to capture the future development of COVID-19 epidemic. We find that the transmission rate inferred by the TDINN frequently fluctuates, and a feedback loop between the epidemic shifting and the changes of transmissibility drives the occurrence of multiple waves. We observe a long response delay to the implementation of control interventions in the four countries, while the decline of the transmission rate in the outbreaks in China usually happens once the implementation of control interventions. The further simulation show that 17 days' delay of the response to the implementation of control interventions lead to a roughly four-fold increase in daily reported cases in one epidemic wave in Italy, which suggest that a rapid response to policies that strengthen control interventions can be effective in flattening the epidemic curve or avoiding subsequent epidemic waves. We observe that the transmission rate in the outbreaks in China is already decreasing before enhancing control interventions, providing the evidence that the increasing of the epidemics can drive self-conscious behavioural changes to protect against infections.