Bayesian particle filter algorithm for learning epidemic dynamics

In this article, we consider a dynamic model for the spread of epidemics, in particular of COVID-19, and the inverse problem of estimating sequentially the time evolution of the unknown state and the model parameters based on noisy observations of the new daily infections. A characteristic of COVID-19 is the significant proportion of secondary infections though contacts with asymptomatic or oligosymptomatic infectious individuals. Since most of these individuals are not accounted for in the number of new daily infections, the size of this cohort can be inferred only indirectly through the underlying model. The evolution model used to propagate the current state from one data instance to the next is a suitably modified SEIR compartment model, providing the expected value for the new daily infection count that is modeled as a Poisson distributed random variable. The estimation of the state and the model parameters is based on a Bayesian particle filtering algorithm. The sequential Bayesian framework naturally provides a quantification of the uncertainty in the estimates of the model parameters, basic reproduction number, and size of the cohorts. Of particular interest is the fact that the algorithm makes it possible to estimate the size of the asymptomatic cohort, a key component for understanding the COVID-19 dynamics, and for planning mitigation measures. Alternative versions of the classical basic reproduction number for estimating the speed of the propagation of the disease are also proposed. The viability of the algorithm is demonstrated through a set of computed examples with both simulated realistic data and actual real data from selected US counties. The numerical tests show that the algorithm reproduces a ratio of asymptomatic vs symptomatic cohort sizes remarkably close to what is currently suggested by the Center for Disease Control.