Discovering the climate dependent disease transmission mechanism through learning-explaining framework

There are evidence showing that meteorological factors, such as temperature and humidity, have critical effects on transmission of some infectious diseases, while quantifying the influence is challenging. In this study we develop a learning-explaining framework to discover the particular dependence of transmission mechanisms on meteorological factors based on multiple source data. The incidence rate based on the epidemic data and epidemic model is theoretically identified, and meanwhile the practical discovery of particular formula is feasible through deep neural networks (DNN), symbolic regression (SR) and sparse identification of nonlinear dynamics (SINDy). In particular, we initially learn the incidence rate in an SIRS model based on epidemic data, then use mechanism discovery methods to explore the possible explicit forms of the incidence rate, and consequently explore the possible relationship between transmission rate and meteorological factors. We finally use information criteria and a definition of evaluation score to make model selection, and hence suggest the optimal explicit formula. We illustrate the idea by derive the incidence rate and transmission rate of respiratory infectious diseases based on the case data on influenza-like illness (ILI) in Xi'an, Shaanxi Province of China and meteorological data from 1st January 2010 to 10th November 2016. The finding reveals that the influence of meteorological factors on transmission exhibits very strong nonlinearity, and modeling the effect should be of great care.