Numerical study of discretization algorithms for stable estimation of disease parameters and epidemic forecasting

In this paper we investigate how various discretization schemes could be incorporated in regularization algorithms for stable parameter estimation and forecasting in epidemiology. Specifically, we compare parametric and nonparametric discretization tools in terms of their impact on the accuracy of recovered disease parameters as well as their impact on future projections of new incidence cases. Both synthetic and real data for 1918 "Spanish Flu" pandemic in San Francisco are considered. The discrete approximation of a time dependent transmission rate is combined with the Levenberg-Marquardt algorithm used to solve the nonlinear least squares problem aimed at fitting the model to limited incidence data for an unfolding outbreak. Our simulation study highlights the crucial role of a priori information at the early stage of an epidemic in mitigating the lack of stability in over-parameterized models with insufficient data. Fortunately, our results suggest that a balanced combination of problem-oriented regularization techniques is one way in which scientists can still draw useful conclusions about system parameters and in turn generate reliable forecasts that policy makers could use to guide control interventions.