The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology
One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this paper, we consider a row of n plants in which m are infected. We then develop a rigorous mathematical approach to investigate the total number of wa...
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| Other Authors: | , , |
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2013
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| Online Access: | http://hdl.handle.net/11073/16695 |
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| _version_ | 1864513437515644928 |
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| author | Al-Sharawi, Ziyad |
| author2 | Burstein, Alexander Deadman, Michael Umar, Abdullahi |
| author2_role | author author author |
| author_facet | Al-Sharawi, Ziyad Burstein, Alexander Deadman, Michael Umar, Abdullahi |
| author_role | author |
| dc.creator.none.fl_str_mv | Al-Sharawi, Ziyad Burstein, Alexander Deadman, Michael Umar, Abdullahi |
| dc.date.none.fl_str_mv | 2013 2020-06-11T11:00:15Z 2020-06-11T11:00:15Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | AlSharawi, Z., Burstein, A., Deadman, M., & Umar, A. (2013). The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology. Journal of Difference Equations and Applications, 19(6), 981–981. https://doi.org/10.1080/10236198.2012.704915 1563-5120 http://hdl.handle.net/11073/16695 10.1080/10236198.2012.704915 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Taylor & Francis |
| dc.relation.none.fl_str_mv | https://doi.org/10.1080/10236198.2012.704915 |
| dc.subject.none.fl_str_mv | Spread of disease Recurrence relation Binomial coefficients Hypergeometric function |
| dc.title.none.fl_str_mv | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology |
| dc.type.none.fl_str_mv | Peer-Reviewed Preprint info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this paper, we consider a row of n plants in which m are infected. We then develop a rigorous mathematical approach to investigate the total number of ways to obtain k isolated individuals among m infected plants. We give a recurrence relation in three parameters that describes the problem, then we find a closed form solution, and give two different approaches to tackle the proof. Finally, we find interesting formulas for the expectation and variance of the random variable that represents the number of infected and isolated plants. |
| format | article |
| id | aus_ff19c169d9644fe9255996af8357a40c |
| identifier_str_mv | AlSharawi, Z., Burstein, A., Deadman, M., & Umar, A. (2013). The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology. Journal of Difference Equations and Applications, 19(6), 981–981. https://doi.org/10.1080/10236198.2012.704915 1563-5120 10.1080/10236198.2012.704915 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16695 |
| publishDate | 2013 |
| publisher.none.fl_str_mv | Taylor & Francis |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiologyAl-Sharawi, ZiyadBurstein, AlexanderDeadman, MichaelUmar, AbdullahiSpread of diseaseRecurrence relationBinomial coefficientsHypergeometric functionOne of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this paper, we consider a row of n plants in which m are infected. We then develop a rigorous mathematical approach to investigate the total number of ways to obtain k isolated individuals among m infected plants. We give a recurrence relation in three parameters that describes the problem, then we find a closed form solution, and give two different approaches to tackle the proof. Finally, we find interesting formulas for the expectation and variance of the random variable that represents the number of infected and isolated plants.Taylor & Francis2020-06-11T11:00:15Z2020-06-11T11:00:15Z2013Peer-ReviewedPreprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAlSharawi, Z., Burstein, A., Deadman, M., & Umar, A. (2013). The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology. Journal of Difference Equations and Applications, 19(6), 981–981. https://doi.org/10.1080/10236198.2012.7049151563-5120http://hdl.handle.net/11073/1669510.1080/10236198.2012.704915en_UShttps://doi.org/10.1080/10236198.2012.704915oai:repository.aus.edu:11073/166952024-08-22T12:01:53Z |
| spellingShingle | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology Al-Sharawi, Ziyad Spread of disease Recurrence relation Binomial coefficients Hypergeometric function |
| status_str | publishedVersion |
| title | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology |
| title_full | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology |
| title_fullStr | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology |
| title_full_unstemmed | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology |
| title_short | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology |
| title_sort | The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology |
| topic | Spread of disease Recurrence relation Binomial coefficients Hypergeometric function |
| url | http://hdl.handle.net/11073/16695 |