# 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 language English 981-993 13 Journal of Difference Equations and Applications 19 6 https://doi.org/10.1080/10236198.2012.704915 Published - 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

### 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.
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