Optimal control of a vectored plant disease model for a crop with continuous replanting

ABSTRACT

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.

KEYWORDS:

• Vectored plant disease
• replanting strategies
• optimal control
• differential equations

Acknowledgments

This work was conducted as a part of the Multiscale Vectored Plant Viruses Investigative Workshop and a short-term visit by VAB and LJSA at the National Institute for Mathematical and Biological Synthesis.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was assisted by a short-term visit and by an investigative workshop on Vectored Plant Viruses at the National Institute for Mathematical and Biological Synthesis, an Institute supported by the National Science Foundation (USA) through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville.