Machine learning mathematical models for incidence estimation during pandemics

Accurate estimates of the incidence of infectious diseases are key for the control of epidemics. However, healthcare systems are often unable to test the population exhaustively, especially when asymptomatic and paucisymptomatic cases are widespread; this leads to significant and systematic under-reporting of the real incidence. Here, we propose a machine learning approach to estimate the incidence of a pandemic in real-time, using reported cases and the overall test rate. In particular, we use Bayesian symbolic regression to automatically learn the closed-form mathematical models that most parsimoniously describe incidence. We develop and validate our models using COVID-19 incidence values for nine different countries, confirming their ability to accurately predict daily incidence. Remarkably, despite the differences in epidemic trajectories and dynamics across countries, we find that a single model for all countries offers a more parsimonious description and is more predictive of actual incidence compared to separate models for each country. Our results show the potential to accurately model incidence in real-time using closed-form mathematical models, providing a valuable tool for public health decision-makers.Author summary: In pandemic situations, adopting timely, effective preventive measures requires accurate and real-time estimates of the incidence of the disease. However, estimates of incidence are typically biased and incomplete. Here, we propose a machine learning method that allows us to discover mathematical models that accurately estimate real incidence from readily available measures, such as the number of cases detected and the number of tests administered on a given day. Contrary to heuristic approaches, which are forced to make bold assumptions about the models, our approach automatically selects the most parsimonious models from the data, with very mild assumptions about the structure of the biases of incidence estimates based on incomplete testing. Our models outperform others at predicting real incidence. Additionally, we find that the same models can be applied to describe nine different countries with very different socioeconomic characteristics and epidemic dynamics.