Abstract
We develop the theory of optimal control for a system of integrodifference equations modelling a pest-pathogen system. Integrodifference equations incorporate continuous space into a system of discrete time equations. We design an objective functional to minimize the damaged cost generated by an invasive species and the cost of controlling the population with a pathogen. Existence, characterization, and uniqueness results for the optimal control and corresponding states have been completed. We use a forwardbackward sweep numerical method to implement our optimization which produces spatio-temporal control strategies for the gypsy moth case study.
| Original language | English |
|---|---|
| Pages (from-to) | 1759-1783 |
| Number of pages | 25 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 20 |
| Issue number | 6 |
| Early online date | 1 Jun 2015 |
| DOIs | |
| Publication status | Published - 1 Aug 2015 |
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Keywords
- Integrodifference equations
- Invasive species
- Optimal control
- Pest-pathogen
Cite this
Optimal control of integrodifference equations in a pest-pathogen system. / Martinez, Marco V.; Lenhart, Suzanne; White, K. A Jane.
In: Discrete and Continuous Dynamical Systems - Series B, Vol. 20, No. 6, 01.08.2015, p. 1759-1783.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Optimal control of integrodifference equations in a pest-pathogen system
AU - Martinez, Marco V.
AU - Lenhart, Suzanne
AU - White, K. A Jane
PY - 2015/8/1
Y1 - 2015/8/1
N2 - We develop the theory of optimal control for a system of integrodifference equations modelling a pest-pathogen system. Integrodifference equations incorporate continuous space into a system of discrete time equations. We design an objective functional to minimize the damaged cost generated by an invasive species and the cost of controlling the population with a pathogen. Existence, characterization, and uniqueness results for the optimal control and corresponding states have been completed. We use a forwardbackward sweep numerical method to implement our optimization which produces spatio-temporal control strategies for the gypsy moth case study.
AB - We develop the theory of optimal control for a system of integrodifference equations modelling a pest-pathogen system. Integrodifference equations incorporate continuous space into a system of discrete time equations. We design an objective functional to minimize the damaged cost generated by an invasive species and the cost of controlling the population with a pathogen. Existence, characterization, and uniqueness results for the optimal control and corresponding states have been completed. We use a forwardbackward sweep numerical method to implement our optimization which produces spatio-temporal control strategies for the gypsy moth case study.
KW - Integrodifference equations
KW - Invasive species
KW - Optimal control
KW - Pest-pathogen
U2 - 10.3934/dcdsb.2015.20.1759
DO - 10.3934/dcdsb.2015.20.1759
M3 - Article
VL - 20
SP - 1759
EP - 1783
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 6
ER -