Journal
JOURNAL OF BIOLOGICAL DYNAMICS
Volume 6, Issue 2, Pages 718-739Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17513758.2012.700074
Keywords
biological control; discrete Hopf bifurcation; uniform persistence; optimal control; Pontryagin's maximum principle
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Funding
- Mathematics Research Promotion Center, National Science Council of Taiwan
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We propose a simple discrete-time host-parasitoid model to investigate the impact of external input of parasitoids upon the host-parasitoid interactions. It is proved that the input of the external parasitoids can eventually eliminate the host population if it is above a threshold and it also decreases the host population level in the unique interior equilibrium. It can simplify the host-parasitoid dynamics when the host population practices contest competition. We then consider a corresponding optimal control problem over a finite time period. We also derive an optimal control model using a chemical as a control for the hosts. Applying the forward-backward sweep method, we solve the optimal control problems numerically and compare the optimal host populations with the host populations when no control is applied. Our study concludes that applying a chemical to eliminate the hosts directly may be a more effective control strategy than using the parasitoids to indirectly suppress the hosts.
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