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
AN - SCOPUS:84879647033
SN - 1023-6198
VL - 19
SP - 981
EP - 993
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 6
ER -