A Unified Framework for Epidemic Prediction based on Poisson Regression

Epidemic prediction is an important problem in epidemic control. Poisson regression methods are often adopted in existing works, mostly with only the (intra-)regional environmental factors considered. As the diffusion of epidemics is affected by not only the intra-regional factors but also inter-regional and external ones, a unified framework based on Poisson regression with the three types of factors incorporated is proposed for the prediction. Specifically, we propose a Poisson-regression-based model first with the intra-regional and inter-regional factors included. The intra-regional factor in a particular time interval is represented by one feature vector with the regionally environmental and social factors considered. The inter-regional factor is modeled by a diffusion matrix which describes the possibilities that the epidemics can spread from one region to another, which in turn accounts for the propagating effects of the infected cases. To learn the structure of the diffusion matrix, we propose two approaches - utilizing some a priori knowledge (e.g., transportation network) and estimating it from scratch via a sparse structure assumption. The resulting optimization problem of the maximum a posterior solution is a convex one and can be efficiently solved by the alternating direction method of multipliers (ADMM). In addition, we incorporate also the external factor, i.e., the imported cases. With one fact that the distribution of the number of infected cases over a year is (approximately) unimodal for most epidemics and one assumption that the importing rate has a small variance over the year, we can approximate the effect of the external factor with a parametric function (e.g., a quadratic function) over time. The resulting optimization problem is still convex and can be also solved by the ADMM algorithm. Empirical evaluations are conducted based on a real data set which records the 16-days-reported cases in the Yunnan province of China for seven years, from 2005 to 2011. The experimental results demonstrate the effectiveness of our proposed models.