Global existence and uniqueness of positive solutions and optimal control for a novel model of pest control

ABSTRACT

In the present paper, a novel model of pest control governed by coupled sets of partial and ordinary differential equations is investigated in detail. Global existence and uniqueness of positive solutions to the above model are obtained. Also, the existence of optimal control is proved, and the first-order and second-order optimality conditions satisfied by optimal control are verified. In particular, the optimal control is demonstrated to be of Bang-Bang form.

KEYWORDS:

• Pest control
• global existence and uniqueness
• positive solutions
• optimal control
• Bang-Bang control

AMS SUBJECT CLASSIFICATIONS (2010):

• 35A01
• 49J20
• 49K20

Acknowledgements

The authors would like to express their gratitude to the anonymous reviewers and editors for their valuable comments and suggestions which led to the improvement of the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NNSF of China [grant number 11571126].