On the usefulness of set-membership estimation in the epidemiology of infectious diseases
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 certai...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018006 |
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| author | Andreas Widder |
| author_facet | Andreas Widder |
| author_sort | Andreas Widder |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d1ad21bb61f5410490810a4795a27d67 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d1ad21bb61f5410490810a4795a27d672025-01-24T02:40:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-01-0115114115210.3934/mbe.2018006On the usefulness of set-membership estimation in the epidemiology of infectious diseasesAndreas Widder0ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, AustriaWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018006mathematical epidemiologyinfectious diseasesode modeset-membership estimationconfidence intervals |
| spellingShingle | Andreas Widder On the usefulness of set-membership estimation in the epidemiology of infectious diseases Mathematical Biosciences and Engineering mathematical epidemiology infectious diseases ode mode set-membership estimation confidence intervals |
| title | On the usefulness of set-membership estimation in the epidemiology of infectious diseases |
| title_full | On the usefulness of set-membership estimation in the epidemiology of infectious diseases |
| title_fullStr | On the usefulness of set-membership estimation in the epidemiology of infectious diseases |
| title_full_unstemmed | On the usefulness of set-membership estimation in the epidemiology of infectious diseases |
| title_short | On the usefulness of set-membership estimation in the epidemiology of infectious diseases |
| title_sort | on the usefulness of set membership estimation in the epidemiology of infectious diseases |
| topic | mathematical epidemiology infectious diseases ode mode set-membership estimation confidence intervals |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018006 |
| work_keys_str_mv | AT andreaswidder ontheusefulnessofsetmembershipestimationintheepidemiologyofinfectiousdiseases |