A Generalized Unscented Transformation for Probability Distributions (preprint)

The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscented transforms developed using either the Gaussian assumption or a minimum set of sigma points typically fall short when the random variable is not Gaussian distributed and the nonlinearities are substantial. In this paper, we develop the generalized unscented transform (GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal components of the skewness and kurtosis tensors of most probability distributions. Constraints can be analytically enforced on the sigma points while guaranteeing at least second-order accuracy. The GenUT uses the same number of sigma points as the original unscented transform while also being applicable to non-Gaussian distributions, including the assimilation of observations in the modeling of infectious diseases such as coronavirus (SARS-CoV-2) causing COVID-19.

Tracking and predicting the African COVID-19 pandemic (preprint)

The ongoing coronavirus disease 2019 (COVID-19) pandemic is heterogeneous throughout Africa and threatening millions of lives. Surveillance and short-term modeling forecasts are critical to provide timely information for decisions on control strategies. We use a model that explains the evolution of the COVID-19 pandemic over time in the entire African continent, parameterized by socioeconomic and geoeconomic variations and the lagged effects of social policy and meteorological history. We observed the effect of the human development index, containment policies, testing capacity, specific humidity, temperature and landlocked status of countries on the local within-country and external between-country transmission. One week forecasts of case numbers from the model were driven by the quality of the reported data. Seeking equitable behavioral and social interventions, balanced with coordinated country-specific strategies in infection suppression, should be a continental priority to control the COVID-19 pandemic in Africa.

Identifiability of infection model parameters early in an epidemic (preprint)

It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series I(t) during the entire epidemic, the parameters can be successfully estimated. In this article we observe that estimation will fail in practice if only infected case data during the early part of the epidemic (pre-peak) is available. This fact can be explained using a long-known phenomenon called dynamical compensation. We use this concept to derive an unidentifiability manifold in the parameter space of SEIR that consists of parameters indistinguishable to I(t) early in the epidemic. Thus, identifiability depends on the extent of the system trajectory that is available for observation. Although the existence of the unidentifiability manifold obstructs the ability to exactly determine the parameters, we suggest that it may be useful for uncertainty quantification purposes. A variant of SEIR recently proposed for COVID-19 modeling is also analyzed, and an analogous unidentifiability surface is derived.

A Poisson Kalman filter for disease surveillance (preprint)

An optimal filter for Poisson observations is developed as a variant of the traditional Kalman filter. Poisson distributions are characteristic of infectious diseases, which model the number of patients recorded as presenting each day to a health care system. We develop both a linear and nonlinear (extended) filter. The methods are applied to a case study of neonatal sepsis and postinfectious hydrocephalus in Africa, using parameters estimated from publicly available data. Our approach is applicable to a broad range of disease dynamics, including both noncommunicable and the inherent nonlinearities of communicable infectious diseases and epidemics such as from COVID-19.