Discovering Mechanistic Correlations Among Respiratory Diseases and Air Quality via Dynamic Modelling Combined with Deep Learning and Symbolic Regression

Air pollution and disease transmission constitute a complex feedback cycle. However, the mechanistic relationship between the variation of air pollution (measured by air quality index (AQI)) and the disease transmission dynamics remains incompletely understood. Here we develop a framework to explore this relationship and we illustrate this framework by inferring the disease transmission rate and inflow rate of air pollutants (IRAP) from AQI and disease incidence data. The coupled system of disease transmission dynamics model and AQI dynamics model is integrated into physics-informed neural networks to embed the information retrieved from the coupled system to the loss function of the neural networks using automatic differentiation, the outcome of this data-driven network for transmission rate and IRAP is then converted into analytic forms of transmission rate and IRAP depending on incidence and AQI, using correlation analyses and symbolic regressions. Based on data from Shaanxi Province of China, this framework is used to establish a linear positive correlation between transmission rate and AQI, and between IRAP and disease incidence. We observe frequent fluctuations in transmission rate and IRAP and show that the mechanistic model with nonlinear analytic forms for transmission rate and IRAP learned through symbolic regression has robust predictive capabilities.