TY - JOUR
T1 - Optimal control of a vectored plant disease model for a crop with continuous replanting
AU - Bokil, V. A.
AU - Allen, L. J.S.
AU - Jeger, M. J.
AU - Lenhart, S.
N1 - Publisher Copyright:
© 2019, © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - Vector-transmitted diseases of plants have had devastating effects on agricultural production worldwide, resulting in drastic reductions in yield for crops such as cotton, soybean, tomato, and cassava. Plant-vector-virus models with continuous replanting are investigated in terms of the effects of selection of cuttings, roguing, and insecticide use on disease prevalence in plants. Previous models are extended to include two replanting strategies: frequencyreplanting and abundance-replanting. In frequency-replanting, replanting of infected cuttings depends on the selection frequency parameter ε, whereas in abundance-replanting, replanting depends on plant abundance via a selection rate parameter also denoted as ε. The two models are analysed and new thresholds for disease elimination are defined for each model. Parameter values for cassava, whiteflies, and African cassava mosaic virus serve as a case study. A numerical sensitivity analysis illustrates how the equilibrium densities of healthy and infected plants vary with parameter values. Optimal control theory is used to investigate the effects of roguing and insecticide use with a goal of maximizing the healthy plants that are harvested. Differences in the control strategies in the two models are seen for large values of ε. Also, the combined strategy of roguing and insecticide use performs better than a single control.
AB - Vector-transmitted diseases of plants have had devastating effects on agricultural production worldwide, resulting in drastic reductions in yield for crops such as cotton, soybean, tomato, and cassava. Plant-vector-virus models with continuous replanting are investigated in terms of the effects of selection of cuttings, roguing, and insecticide use on disease prevalence in plants. Previous models are extended to include two replanting strategies: frequencyreplanting and abundance-replanting. In frequency-replanting, replanting of infected cuttings depends on the selection frequency parameter ε, whereas in abundance-replanting, replanting depends on plant abundance via a selection rate parameter also denoted as ε. The two models are analysed and new thresholds for disease elimination are defined for each model. Parameter values for cassava, whiteflies, and African cassava mosaic virus serve as a case study. A numerical sensitivity analysis illustrates how the equilibrium densities of healthy and infected plants vary with parameter values. Optimal control theory is used to investigate the effects of roguing and insecticide use with a goal of maximizing the healthy plants that are harvested. Differences in the control strategies in the two models are seen for large values of ε. Also, the combined strategy of roguing and insecticide use performs better than a single control.
KW - Vectored plant disease
KW - differential equations
KW - optimal control
KW - replanting strategies
UR - http://www.scopus.com/inward/record.url?scp=85066623876&partnerID=8YFLogxK
U2 - 10.1080/17513758.2019.1622808
DO - 10.1080/17513758.2019.1622808
M3 - Article
C2 - 31149889
AN - SCOPUS:85066623876
SN - 1751-3758
VL - 13
SP - 325
EP - 353
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
IS - sup1
ER -