Abstract
AbstractImproving 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.
Highlights
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
The problem has often to be faced with tight constraints imposed on the budget allocated on species removal programs
A model‐driven approach to the problem would allow for the optimization of available efforts and to perform a scenario analysis in environmental conditions, which may vary due to external drivers
Summary
Due to Proposition 3.3, for each E ∈ there exists a unique function n = n (E) in L2 (0, T, H1 (Ω)), which satisfies (4) and (5) and represents the weak solution of state Equations (1) and (2). We provide the sensitivity equation and the adjoint problem and we obtain a relationship which characterizes the optimal control.
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