Optimal spatiotemporal effort allocation for invasive species removal incorporating a removal handling time and budget

Abstract

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.

Geometric Numerical Integration in Ecological Modelling

“…was compared with EXPP in (16) and IMSP given in (19). The results are shown in Figures 5-7 and summarized below.…”

“…In [16], a reaction-diffusion partial differential equation models the spatiotemporal dynamics of the invasion of alien fish population inside a very complex geometry representing a realistic lake and the optimal control theory has been applied to obtain the optimal management strategy with a given budget constraint. The model describes a complex and realistic situation by including a control term that has Holling-II type behavior, a budget constraint and the habitat suitability function which represents the suitability of habitat for a given species based on known affinities with environmental parameters.…”

“…In [16] a control action over a time horizon with length T = 4 for the invasion of an alien fish population inside the hypothetical lake is simulated. A penalty term weighted by coefficient c = 0.22 for the budget constraint 0 ≤ E ≤ B = 0.5 was set.…”

“…Limiting to first-order procedures, we will illustrate the most suitable geometric numerical integrators for some ecosystem dynamics models. For optimal control problems that model management policies, we will describe the advantage of the symplectic Runge-Kutta pairs in order to get efficient methods easy to be implemented within any numerical software [16]. Finally, as future perspective, we will present some examples of ecological models featured by both Poisson and biochemical structure [17] and we will discuss about some open questions related to their numerical approximation.…”

Optimal fishery with coastal catch

“…In a number of bioeconomic and resource‐economic papers (e.g., Baker, Diele, Marangi, Martiradonna, & Ragni, ; Ding & Lenhart, ; Fister & Lenhart, ; Fister, ; Kelly, Xing, & Lenhart, ; Lenhart, Liang, & Protopopescu, ), the existence of OCs, and subsequently the validity of the Pontryagin's maximum principle, has been proven on a case by case basis using some minimizing sequence and compactness arguments (see also Aniţa et al, , chapter 5; Lenhart & Workman, , chapter 25). However, all these studies consider steady problems or finite time horizons.…”