The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology

Z. AlSharawi, A. Burstein, M. Deadman, A. Umar

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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 study, 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 formulae for the expectation and variance of the random variable that represents the number of infected and isolated plants.

Original languageEnglish
Pages (from-to)981-993
Number of pages13
JournalJournal of Difference Equations and Applications
Volume19
Issue number6
DOIs
Publication statusPublished - 2013

Fingerprint

Recursive Sequence
Epidemiology
Combinatorial Problems
Random processes
Random variables
Crops
Random process
Recurrence relation
Closed-form Solution
Random variable

Keywords

  • binomial coefficients
  • hypergeometric function
  • recurrence relation
  • spread of disease

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Analysis

Cite this

The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology. / AlSharawi, Z.; Burstein, A.; Deadman, M.; Umar, A.

In: Journal of Difference Equations and Applications, Vol. 19, No. 6, 2013, p. 981-993.

Research output: Contribution to journalArticle

AlSharawi, Z. ; Burstein, A. ; Deadman, M. ; Umar, A. / The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology. In: Journal of Difference Equations and Applications. 2013 ; Vol. 19, No. 6. pp. 981-993.
@article{5f155898a5cb424c924124099dae0640,
title = "The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology",
abstract = "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 study, 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 formulae for the expectation and variance of the random variable that represents the number of infected and isolated plants.",
keywords = "binomial coefficients, hypergeometric function, recurrence relation, spread of disease",
author = "Z. AlSharawi and A. Burstein and M. Deadman and A. Umar",
year = "2013",
doi = "10.1080/10236198.2012.704915",
language = "English",
volume = "19",
pages = "981--993",
journal = "Journal of Difference Equations and Applications",
issn = "1023-6198",
publisher = "Taylor and Francis Ltd.",
number = "6",

}

TY - JOUR

T1 - The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology

AU - AlSharawi, Z.

AU - Burstein, A.

AU - Deadman, M.

AU - Umar, A.

PY - 2013

Y1 - 2013

N2 - 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 study, 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 formulae for the expectation and variance of the random variable that represents the number of infected and isolated plants.

AB - 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 study, 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 formulae for the expectation and variance of the random variable that represents the number of infected and isolated plants.

KW - binomial coefficients

KW - hypergeometric function

KW - recurrence relation

KW - spread of disease

UR - http://www.scopus.com/inward/record.url?scp=84879647033&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879647033&partnerID=8YFLogxK

U2 - 10.1080/10236198.2012.704915

DO - 10.1080/10236198.2012.704915

M3 - Article

VL - 19

SP - 981

EP - 993

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

IS - 6

ER -