Poisson Kalman filter for disease surveillance

Open Access

Poisson Kalman filter for disease surveillance

Donald Ebeigbe, Tyrus Berry, Steven J. Schiff, and Timothy Sauer

Phys. Rev. Research 2, 043028 – Published 6 October 2020

Abstract

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 a 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.

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Received 24 March 2020
Accepted 13 September 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043028

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Bacterial infections Diseases, physiology & pathology Epidemic Optimization problems

Stochastic dynamical systems

Interdisciplinary Physics

Authors & Affiliations

Donald Ebeigbe ^1,*, Tyrus Berry ^2,*, Steven J. Schiff ^1,3, and Timothy Sauer ²

¹Center for Neural Engineering, Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
²Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA
³Center for Infectious Disease Dynamics, Pennsylvania State University, University Park, Pennsylvania 16802, USA; Department of Neurosurgery, Penn State College of Medicine, Pennsylvania State University, Hershey, Pennsylvania 17033, USA; and Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16801, USA

^*These authors contributed equally to this work.

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Vol. 2, Iss. 4 — October - December 2020

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