On the usefulness of set-membership estimation in the epidemiology of infectious diseases

Andreas Widder; Andreas Widder

doi:10.3934/mbe.2018006

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 1: 141-152. doi: 10.3934/mbe.2018006

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On the usefulness of set-membership estimation in the epidemiology of infectious diseases

Andreas Widder

ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria

Received: 12 September 2016 Accepted: 14 March 2017 Published: 01 February 2018
MSC : 92D30, 49J53, 34H99, 90C30

We present a method, known in control theory, to give set-membership estimates for the states of a population in which an infectious disease is spreading. An estimation is reasonable due to the fact that the parameters of the equations describing the dynamics of the disease are not known with certainty. We discuss the properties of the resulting estimations. These include the possibility to determine best-or worst-case-scenarios and identify under which circumstances they occur, as well as a method to calculate confidence intervals for disease trajectories under sparse data. We give numerical examples of the technique using data from the 2014 outbreak of the Ebola virus in Africa. We conclude that the method presented here can be used to extract additional information from epidemiological data.
- Mathematical epidemiology,
- infectious diseases,
- ODE mode,
- set-membership estimation,
- confidence intervals
Citation: Andreas Widder. On the usefulness of set-membership estimation in the epidemiology of infectious diseases[J]. Mathematical Biosciences and Engineering, 2018, 15(1): 141-152. doi: 10.3934/mbe.2018006

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Abstract

We present a method, known in control theory, to give set-membership estimates for the states of a population in which an infectious disease is spreading. An estimation is reasonable due to the fact that the parameters of the equations describing the dynamics of the disease are not known with certainty. We discuss the properties of the resulting estimations. These include the possibility to determine best-or worst-case-scenarios and identify under which circumstances they occur, as well as a method to calculate confidence intervals for disease trajectories under sparse data. We give numerical examples of the technique using data from the 2014 outbreak of the Ebola virus in Africa. We conclude that the method presented here can be used to extract additional information from epidemiological data.

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