A viability analysis of sustainable by-catch fisheries under direct conservation measures

<p>Sustainability in fisheries is a complex concept and one that has attracted a rich history of research over time. The basic concerns of sustainability are how to reconcile ecological, economic and social requirements within the perspectives of intra- and inter-generational equity. Therefore, maintaining these requirements simultaneously is critical to achieving a perennial system and avoiding so-called “crisis” situations. It is contended that viability theory, which is a relatively new area of mathematics, rigorously captures the essence of sustainability. Using viability theory, this thesis develops two viability models based on different direct conservation measures (i.e. input and output controls) to examine the feasibility conditions under which a regulator can achieve sustainability in a fishery characterised by a “by-catch process”, whereby one species is targeted and another species is incidentally caught as by-catch. The first model considers a by-catch fishery where fishing input is controlled by a regulator. The second model considers two interrelated fisheries managed using a dual quantity-price system, which is based on New Zealand’s Quota Management System (QMS). For each model, the set of constraints representing the “good health” of the system are characterised using managerial priorities identified in the literature. Then, the viability kernel, which is the largest set of initial states for which there are controls that result in inter-temporal trajectories satisfying all the constraints, is approximated numerically. This is achieved by employing VIKAASA, which is a computer application capable of generating kernel approximations. The viability kernel provides the regulator with meaningful reference values and indicators for desirable or undesirable states of the fishery, which serve as important inputs into policy decisions. This study also shows the potential for viability theory to provide policy makers with a better insight of how to integrate ecosystem considerations into the QMS.</p>

A viability analysis of sustainable by-catch fisheries under direct conservation measures

<p>Sustainability in fisheries is a complex concept and one that has attracted a rich history of research over time. The basic concerns of sustainability are how to reconcile ecological, economic and social requirements within the perspectives of intra- and inter-generational equity. Therefore, maintaining these requirements simultaneously is critical to achieving a perennial system and avoiding so-called “crisis” situations. It is contended that viability theory, which is a relatively new area of mathematics, rigorously captures the essence of sustainability. Using viability theory, this thesis develops two viability models based on different direct conservation measures (i.e. input and output controls) to examine the feasibility conditions under which a regulator can achieve sustainability in a fishery characterised by a “by-catch process”, whereby one species is targeted and another species is incidentally caught as by-catch. The first model considers a by-catch fishery where fishing input is controlled by a regulator. The second model considers two interrelated fisheries managed using a dual quantity-price system, which is based on New Zealand’s Quota Management System (QMS). For each model, the set of constraints representing the “good health” of the system are characterised using managerial priorities identified in the literature. Then, the viability kernel, which is the largest set of initial states for which there are controls that result in inter-temporal trajectories satisfying all the constraints, is approximated numerically. This is achieved by employing VIKAASA, which is a computer application capable of generating kernel approximations. The viability kernel provides the regulator with meaningful reference values and indicators for desirable or undesirable states of the fishery, which serve as important inputs into policy decisions. This study also shows the potential for viability theory to provide policy makers with a better insight of how to integrate ecosystem considerations into the QMS.</p>

Process Performance Verification Using Viability Theory

The development of efficient methods for process performance verification has drawn a lot of attention in the research community. Viability theory is a mathematical tool to identify the trajectories of a dynamical system which remains in a constraint set. In this paper, viability theory is investigated for this purpose in the case of nonlinear processes that can be represented in Linear Parameter Varying (LPV) form. In particular, verification algorithms based on the use of invariance and viability kernels and capture basin are proposed. The difficulty with the application of this theory is the computation of these sets. A Lagrangian method has been used to approximate these sets. Because of simplicity and efficient computations, zonotopes are adopted for set representation. Two new sets called Safe Work Area (SWA) and Required Performance (RP) are defined and an algorithm is proposed to use these concepts for the verification purpose. Finally, two application examples based on well-known case studies, a two-tank system and PH neutralization plant, are provided to show the effectiveness of the proposed method.

Articulating bargaining theories: movement, chance, and necessity as descriptive principles

The Nash Demand Game (NDG) has been one of the first models (Nash in Econometrica 21(1):128–140, 1953. 10.2307/1906951) that has tried to describe the process of negotiation, competition, and cooperation. This model has had enormous repercussions and has leveraged basic and applied research on bargaining processes. Therefore, we wonder whether it is possible to articulate extensive and multiple developments into a single unifying framework. The Viability Theory has this inclusive approach. Thus, we investigate the NDG under this point of view, and, carrying out this work, we find that the answer is not only affirmative but that we also advance in characterising viable NDGs. In particular, we found foundations describe the distributive Bargaining Theory: the principle of movement and the principle of chance and necessity. Finally, this initial work has many interesting perspectives. The probably most important idea is to integrate developments of the Bargaining Theory and thus capture the complexity of the real world in an articulated way.

Set-Valued Control Approach Applied to a COVID-19 Model with Screening and Saturated Treatment Function

The purpose of this paper is modelling and controlling the spread of COVID-19 disease in Morocco. A nonlinear mathematical model with two subclasses of infectious individuals is proposed. The population is divided into five classes, namely, susceptible (S), exposed (E), undiagnosed infectious ( I n c ), diagnosed patients ( I c ), and removed individuals. To reflect the real dynamic of the COVID-19 transmission in Morocco, the real reported data are used for estimating model parameters. Two controls representing screening effort and limited treatment are considered. Based on viability theory and set-valued analysis, a Lyapunov function is constructed such that both exposed and infected populations are decreased to zero asymptotically. The corresponding controls are derived via a continuous selection of adequately designed feedback map. Numerical simulations are presented with three scenarios (cases when each control is used alone and the case when two controls are combined). Our results show that when only one control is to be applied, screening is the most effective in decreasing the number of people in the three infected compartments, whereas combining both controls is found to be highly effective and leads to a significant improvement in the epidemiological situation of Morocco. To the best of our knowledge, this work is the first one that applies the set-valued approach to a controlled COVID-19 model which agrees with the observed cases in Morocco.