A network theoretic method for the basic reproductive number for infectious diseases
Abstract When an outbreak of an infectious disease occurs, whether it is COVID‐19 in humans, pine wilt in trees or canine distemper in dogs, quick and decisive actions need to be taken to contain it. One tool that can help both the scientific and applied management communities understand the infecti...
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| Format: | Article |
| Language: | English |
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Wiley
2022-11-01
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| Series: | Methods in Ecology and Evolution |
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| Online Access: | https://doi.org/10.1111/2041-210X.13978 |
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| author | Anna Sisk Nina Fefferman |
| author_facet | Anna Sisk Nina Fefferman |
| author_sort | Anna Sisk |
| collection | DOAJ |
| description | Abstract When an outbreak of an infectious disease occurs, whether it is COVID‐19 in humans, pine wilt in trees or canine distemper in dogs, quick and decisive actions need to be taken to contain it. One tool that can help both the scientific and applied management communities understand the infection risk during an outbreak is the basic reproductive number, ℛ0. In this paper, we use a network method to calculate and analyse the basic reproductive number, specifically flow network theory. We convert traditional compartmental models to flow networks and then apply the fundamental Max‐Flow Min‐Cut Theorem to calculate the basic reproductive number. We show that this method is equivalent to the traditional next generation matrix method for the calculation of ℛ0, and thus a valid alternative. Then we provide step‐by‐step instructions and illustrate how to apply this method to epidemic models. The current methods available for calculating ℛ0 are complicated, requiring mathematical training. This can act as a barrier to understanding and cause delays in a real‐time response. Our new approach drastically reduces the mathematical complexity of the calculation and is far more accessible to the broader scientific community. It also allows for novel insights and can be applied to models/situations where traditional methods fail. |
| format | Article |
| id | doaj-art-e071f0524d0345cb8eb1d45cc8f73d5e |
| institution | DOAJ |
| issn | 2041-210X |
| language | English |
| publishDate | 2022-11-01 |
| publisher | Wiley |
| record_format | Article |
| series | Methods in Ecology and Evolution |
| spelling | doaj-art-e071f0524d0345cb8eb1d45cc8f73d5e2025-08-20T03:23:30ZengWileyMethods in Ecology and Evolution2041-210X2022-11-0113112503251510.1111/2041-210X.13978A network theoretic method for the basic reproductive number for infectious diseasesAnna Sisk0Nina Fefferman1Department of Mathematics University of Tennessee Knoxville Tennessee USADepartment of Mathematics University of Tennessee Knoxville Tennessee USAAbstract When an outbreak of an infectious disease occurs, whether it is COVID‐19 in humans, pine wilt in trees or canine distemper in dogs, quick and decisive actions need to be taken to contain it. One tool that can help both the scientific and applied management communities understand the infection risk during an outbreak is the basic reproductive number, ℛ0. In this paper, we use a network method to calculate and analyse the basic reproductive number, specifically flow network theory. We convert traditional compartmental models to flow networks and then apply the fundamental Max‐Flow Min‐Cut Theorem to calculate the basic reproductive number. We show that this method is equivalent to the traditional next generation matrix method for the calculation of ℛ0, and thus a valid alternative. Then we provide step‐by‐step instructions and illustrate how to apply this method to epidemic models. The current methods available for calculating ℛ0 are complicated, requiring mathematical training. This can act as a barrier to understanding and cause delays in a real‐time response. Our new approach drastically reduces the mathematical complexity of the calculation and is far more accessible to the broader scientific community. It also allows for novel insights and can be applied to models/situations where traditional methods fail.https://doi.org/10.1111/2041-210X.13978epidemic thresholdepidemiological thresholdgraphical algorithmnetwork calculation |
| spellingShingle | Anna Sisk Nina Fefferman A network theoretic method for the basic reproductive number for infectious diseases Methods in Ecology and Evolution epidemic threshold epidemiological threshold graphical algorithm network calculation |
| title | A network theoretic method for the basic reproductive number for infectious diseases |
| title_full | A network theoretic method for the basic reproductive number for infectious diseases |
| title_fullStr | A network theoretic method for the basic reproductive number for infectious diseases |
| title_full_unstemmed | A network theoretic method for the basic reproductive number for infectious diseases |
| title_short | A network theoretic method for the basic reproductive number for infectious diseases |
| title_sort | network theoretic method for the basic reproductive number for infectious diseases |
| topic | epidemic threshold epidemiological threshold graphical algorithm network calculation |
| url | https://doi.org/10.1111/2041-210X.13978 |
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