Open AccessOptimal spatiotemporal effort allocation for invasive species removal incorporating a removal handling time and budget
Author(s) -
Baker Christopher M.,
Diele Fasma,
Marangi Carmela,
Martiradonna Angela,
Ragni Stefania
Publication year - 2018
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/nrm.12190
Subject(s) - mathematical optimization , computer science , budget constraint , optimal control , constraint (computer aided design) , extinction (optical mineralogy) , control (management) , optimal allocation , operations research , mathematics , artificial intelligence , economics , physics , geometry , neoclassical economics , optics
Improving strategies for the control and eradication of invasive species is an important aspect of nature conservation, an aspect where mathematical modeling and optimization play an important role. In this paper, we introduce a reaction‐diffusion partial differential equation to model the spatiotemporal dynamics of an invasive species, and we use optimal control theory to solve for optimal management, while implementing a budget constraint. We perform an analytical study of the model properties, including the well‐posedness of the problem. We apply this to two hypothetical but realistic problems involving plant and animal invasive species. This allows us to determine the optimal space and time allocation of the efforts, as well as the final length of the removal program so as to reach the local extinction of the species.