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In this paper, we propose to study a fishery model with variable price. We assume that the price evolves much faster than the rest of the system. Under certain assumptions, this makes it possible to consider the fishery system as a slow–fast system, on two time scales, and to study it with a reduced model of dimension two. Two main cases can occur. The first one which we called catastrophic equilibrium corresponds to over-exploitation leading to fish extinction and a booming price. The second case corresponds to a sustainable fishery equilibrium which is stable. The possible effects of the creation of marine protected areas (MPAs), sites where fishing is prohibited, on the fish stock and fishery are evaluated. We show that MPAs can have a positive effect on the restoration of depleted fish stocks by destabilizing the catastrophic equilibrium and keeping only one positive equilibrium which will be globally asymptotically stable. This problem is addressed by proposing a model with MPA for the fish dynamics. Fish are assumed to move between MPA and fishing area and are subject to harvesting through fishing. We show that to avoid the extinction of the stock and stabilize the fishery in the long term, it is necessary to define a fishing zone such that the ratio of its carrying capacity to its surface is small enough. We further show that with a judicious choice of the surface area of the MPA, it is possible to optimize the total capture.

We propose an SIR epidemic model taking into account prevention measures against coronavirus disease 2019 (COVID-19) such as wearing masks and respecting safety distances. We look for the conditions to avoid a second epidemic peak in the phase of release from confinement. We derive equations for the critical levels of mask efficiency, mask adoption (fraction of population wearing masks) and fraction of population engaging in physical distancing that lower the basic reproduction number ℜ0 to unity. Conclusions: For ℜ0 = 2.5, if at least 40% of people wear masks with efficiency 50%, and at least 20% of the population without masks (or anti-maskers) respect physical distancing measures, the effective reproduction number can be reduced to less than 1 and COVID-19 infections would plummet. The model predicts also that if at least half of the people respecting physical distancing, COVID-19 outbreaks with ℜ0 of about 3, would be theoretically extinguished without wearing masks. The results of this study provide an alternative explanation for the spread of the disease, and suggest some valuable policy recommendations about the control strategies applied to mitigate disease transmission.

International audience; Palladium isolation and refining through solvent extraction suffer from limited stability of commercial reagents or limited availability of robust reagents in nitrate media. Several performing extraction solvents based on diamide reagents have been proposed, but their preparation requires synthetic chemistry skills. In the present work, we propose the use of readily accessible N,N,N',N'-tetrahexylmalonamide (THMA). This reagent revealed superior distribution ratios and selectivity in comparison with previously used diamides for palladium(II) extraction from nitrate media in the frame of palladium recovery from waste. Furthermore, the benefit of excess dihexylamine (DHA) employed during the preparation of THMA was demonstrated through a gain in kinetics performance. Detailed analysis enabled to determine the best performing formulation of extraction solvent, which can be readily prepared from commercially available chemicals without any complex synthesis procedure nor purification step.

In this paper we develop a non-autonomous predator-prey system with time delay to study the influence of water level fluctuations on the interactions between fish species living in an artificial lake. We derive persistence and extinction conditions of the species. Using coincidence degree theory, we determine conditions for which the system has at least one periodic solution. Numerical simulations are presented to illustrate theoretical results.

Wir schlagen ein System gewöhnlicher Differentialgleichungen mit homogenen nichtlinearen Termen des ersten Grades vor, um den demografischen Übergang zu modellieren. Es gibt zwei Altersgruppen und zwei Fruchtbarkeitsstufen. Eine geringe Fruchtbarkeit erstreckt sich durch Mimikry auf Erwachsene mit hoher Fruchtbarkeit. Wenn der Mimikry-Koeffizient zunimmt, überschreitet die Bevölkerung zwei Schwellenwerte. Zwischen diesen beiden Schwellenwerten nimmt die Population mit einer stabilen Mischung der beiden Fertilitätsraten exponentiell zu oder ab. Dieser teilweise demografische Übergang ist in einigen Ländern Afrikas südlich der Sahara zu beobachten. We study a mathematical model for the demographic transition. It is a homogeneous differential system of degree one. There are two age groups and two fertility levels. Low fertility extends by mimicry to adults with high fertility. When the mimicry coefficient increases, the system crosses two thresholds between which the population increases or decreases exponentially with a stable mixture of the two fertility rates. This partial demographic transition is reminiscent of the situation in some countries of sub-Saharan Africa. On propose un système d'équations différentielles ordinaires avec des termes non linéaires homogènes de degré un pour modéliser la transition démographique. Il y a deux classes d'âge et deux niveaux de fécondité. La fécondité faible s'étend par mimétisme aux adultes avec une fécondité élevée. Lorsque le coefficient de mimétisme augmente, la population traverse deux seuils. Entre ces deux seuils, la population croît ou décroît exponentiellement avec un mélange stable des deux fécondités. Cette transition démographique partielle s'observe dans certains pays d'Afrique subsaharienne.

We present a classic SEIR model taking into account the daily movements of individuals in different places. The model also takes into account partial confinement of individuals. This model is coupled with a model of protection against the epidemic by the use of masks. We are studying the effects of combined confinement and protection measures on the dynamics of the epidemic. We consider a constant proportion of asymptomatic people. We assume that symptomatic infected people may change their urban travel behavior due to the disease which causes them to travel less to places where they used to move and to stay at home more often. We present a sensitivity study with respect to the parameters. We show that the combination of the use of masks with almost complete release of confinement makes it possible to avoid the occurrence of a secondary peak of the epidemic. The model predicts that a total release of confinement can be successful for an epidemic of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0 = 2.5$$\end{document}R0=2.5 if on average a proportion of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$60\%$$\end{document}60% of the population wears masks of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$60\%$$\end{document}60% efficacy. However, if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\%$$\end{document}10% of the population remains confined, the same goal can be achieved with a proportion of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$80\%$$\end{document}80% of the population wearing masks with efficacy of the order of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$40\%$$\end{document}40%.

International audience; In this paper, we use the exponential transform to give a unified formal upper bound for the asymptotic rate of spread of a population propagating in a one dimensional habitat. We show through examples how this upper bound can be obtained directly for discrete and continuous time models. This upper bound has the form min s>0 ln(ρ(s))/s and coincides with the speeds of several models found in the literature. 1. Introduction. Under favourable biological conditions, a well or newly established population in a one dimensional continuous habitat (e.g. coastline [24], river [27], a preferred direction in a multidimensional space), can spread at left (in the region x ≤ 0), at right (in the region x ≥ 0) or in both directions causing direct and indirect effects on the ecosystem [44, 7, 10, 14]. One important measure quantifying this spread is the asymptotic speed of propagation of the expanding population in the environment, generally called the invasion speed when dealing with the spread of invasive species [13]. This asymptotic quantity has been studied for a large class of biological models like reaction-diffusion [9, 1, 4, 19, 35], integrodifferential [30, 28], integrodifference [18, 42] and discrete-time recursion [48, 25] equations. A mathematical formulation of the asymptotic speed of spread (in short, spreading speed) appeared in the work of Aronson and Weinberger [1] on the Fisher-KPP reaction-diffusion equation under specific conditions. They showed that the solutions N (t, x) (population density at time t and position x) travel in a one dimensional habitat of carrying capacity unity with a spreading speed c * > 0 characterized by the behaviour of N (t, ξ + ct) for large t, where ξ and c are real numbers. More precisely, for some α ∈ (0, 1] and every ξ, it holds

The first case of coronavirus disease 2019 (COVID-19) in Algeria was reported on 25 February 2020. Since then, it has progressed rapidly and the number of cases grow exponentially each day. In this article, we utilize SEIR modelling to forecast COVID-19 outbreak in Algeria under two scenarios by using the real-time data from March 01 to April 10, 2020. In the first scenario: no control measures are put into place, we estimate that the basic reproduction number for the epidemic in Algeria is 2.1, the number of new cases in Algeria will peak from around late May to early June and up to 82% of the Algerian population will likely contract the coronavirus. In the second scenario, at a certain date T, drastic control measures are taken, people are being advised to self-isolate or to quarantine and will be able to leave their homes only if necessary. We use SEIR model with fast change between fully protected and risky states. We prove that the final size of the epidemic depends strongly on the cumulative number of cases at the date when we implement intervention and on the fraction of the population in confinement. Our analysis shows that the longer we wait, the worse the situation will be and this very quickly produces.

A periodic predator-prey model has been introduced in [5] to study the effect of water level on persistence or extinction of fish populations living in an artificial lake. By using the continuation theorem of Mawhin’s coincidence degree theory, the authors give sufficient conditions for the existence of at least one positive periodic solution. In this paper we study the problem in the general case. We begin by analyzing the invariance, permanence, non-persistence and the globally asymptotic stability for the system. Most interestingly, under additional conditions, we find that the periodic solution obtained in [5] is unique. Finally, in order to make the model system more realistic, we consider the special case when the periodicity in [5] is replaced by almost periodicity. We obtain conditions for existence, uniqueness and stability of a positive almost periodic solution. The methods used in this paper will be comparison theorems and Lyapunov functions. An example is employed to illustrate our result.

A cleaner and eco-friendly method was developed for the preparation of tetrakis(aminomethyl)calix-[4]-resorcinarene via a synthetic pathway of five steps starting from methylresorcinol. This alternative methodology is firstly based on avoiding the use of CH2BrCl, which is a non-eco-friendly substance with high ozone depletion potential, and on replacing it by CH2Cl2 as a readily available reagent with much less dangerous effects. Secondly, this method engages acetone or CH2Cl2 as the solvent of the bromination step in the place of the very toxic CCl4, leading to tetrakis(bromomethyl)calix-[4]-resorcinarene. The brominated intermediate has been reacted with sodium azide in acetone instead of the high-boiling solvent DMSO to produce tetrakis(azidomethyl) calix-[4]-resorcinarene without the need of tedious purification. Lastly, this work reports an efficient hydrogenation method of the versatile azido adduct employing Pt/C (5%) as the catalyst for the preparation of the amino cavitand as an alternative route with high atom economy that can replace the classical methods used currently.

In this paper, we study a mathematical bio-economic model of a fishery with varying price. The three dimensional model describes the time evolution of the resource, the fishing effort and the price. The model is original because it considers a nonlinear harvesting function assumed to depend upon stock size and fishing effort with a saturation effect with respect to the resource as well as a price equation depending on demand and supply which is in addition proportional to price. Assuming that the price varies at a fast time scale, we are able to use ”aggregation of variables methods” in order to reduce the model in a two dimensional model at a slow time scale. This aggregated (reduced) model is analyzed. Several numerical simulations of the model are performed to substantiate our analytical findings. The existence of nonlinear harvesting makes the dynamics of the model more complicated, including multiple equilibria, bi-stability and limit cycle. Such large amplitude cycle variations are not desirable because they generate periods of overfishing at periods of very low activity. We then study the effects of marine reserves on the dynamics of the fishery, showing that for an adequate number of small reserves, limit cycle oscillations are switched off.

In lakes, water level can alter the physical environment and may influence predatory fish performance. In this paper, we ask how do variations in water level affect population cycles? We use a predator-prey model that includes fishing terms as a case study. With the help of a continuation theorem based on Gaines and Mawhin’s coincidence degree, we establish sufficient conditions for the existence of at least four positive periodic solutions. Our theoretical results confirm the assumption that the water level exerts a strong influence on the interaction between fishes. An example is given to illustrate the effectiveness of our results.

The Routh–Hurwitz stability criterion is a useful tool for investigating the stability property of linear and nonlinear dynamical systems by analyzing the coefficients of the corresponding characteristic polynomial without calculating the eigenvalues of its Jacobian matrix. Recently some of these conditions have been generalized to fractional systems of order α ∈ [0, 1). In this paper we extend these results to fractional systems of order α ∈ [0, 2). Stability diagram and phase portraits classification in the (τ, Δ)-plane for planer fractional-order system are reported. Finally some numerical examples from population dynamics are employed to illustrate our theoretical results.

The main concern of this paper is to study the dynamic of a predator-prey system with diffusion. It incorporates the Holling-type-II and a modified Leslie-Gower functional responses under Robin boundary conditions. More concretely, we study the dissipativeness of the system by using the comparison principle, and we derive a criteria for permanence and for predator extinction.

This paper describes a fish prey–predator model with a new functional response. The dynamics of the system is discussed mainly from the point of view of permanence and stability. We obtain conditions that affect the persistence of the system. Local asymptotic stability of various equilibrium solutions is explored to understand the dynamics of the model system. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional. We then examine possibilities of the existence of bionomic equilibrium. Lastly, the optimal harvesting policy is obtained by using the Pontryagin’s maximum principle. The objective is to maximize the monetary social benefit as well as conservation of the ecosystem.

The present paper deals with an Holling-Type-II predator-prey model incorporating a seasonal harvest of the prey and migration of predator. The model describes the interaction between migratory bird population as the predator and the fish population as prey. Some sufficient conditions are obtained for permanence and global asymptotical stability of the system by using the comparison theorem and constructing a suitable Lyapunov function. By using the continuation theorem of coincidence degree theory, sufficient condition for existence of a positive periodic solution is established. Some computational results have been addressed.

This paper addresses the problem of the optimal size and number of marine reserves to achieve maximum value in commercial fisheries. A simplified network planning situation is analyzed to optimize the size and number of marine reserves. We consider a general 2L-patch model of harvesting population dynamics with continuous time. Fish movements between the sites, as well as vessel displacements between the fishing sites, are assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and the total fishing effort. This reduced model is used to determine the optimal size and number of a marine reserves in order to maximize the catch at equilibrium. We show that the optimal number that maximizes the total fish catch at equilibrium depend intricately on the size of the reserve: A small number of reserves is optimal when the size of the reserve is higher and inverse.

Prey–predator interactions are influenced by many ecological factors. In this paper, a delayed periodic prey–predator model with instantaneous negative feedback is investigated to study the impact of water level on persistence of two fish populations living in an artificial lake. By using the continuation theorem of coincidence degree theory, and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions is derived for the existence, uniqueness and global stability of positive periodic solutions to the model. Numerical simulation is carried out to illustrate the feasibility of our main results.

Habitat fragmentation is generally believed to be detrimental to the persistence of natural populations. In nature management one therefore tends to prefer many small nature reserves over one single large having equal total area. The paper presents two tractable analytical models to examine whether this preference is warranted in a metapopulation framework with reserves (patches) by formulating the dependence of the density as well as the global catch on the number of reserves. Studying these models, we seek to compare the two different strategies: whether a single large reserve will (1) conserve more species and (2) maintains high yield in fisheries than several small or vice versa? Our results indicate that it is favourable to make several small reserves instead one single large reserve. Indeed, at equilibrium, the density as well as the global catch are bigger in the Several Small (SS) strategy than in the Single Large (SL) one. In addition, in the case of SS strategy, an intermediate reserve number exists which is optimal for catch at equilibrium. The results in this paper may provide important implications for nature conservation.

Mobile ad hoc networks (MANET) are a subclass of wireless and mobile networks. All nodes in MANET are mobile and they communicate with each other without fixed infrastructures. The QoS (Quality of Services) routing is one of the recent most challenges for mobile ad hoc networks. Several works have been proposed to address this challenge. The major problem of these works is that they do not consider the stability of paths in their paths establishment process. For this, the routing based on link stability has become a challenge. Several factors can influence on the paths stability such as the mobility of nodes belonging to the path, the path overhead, and the residual energy of nodes constituting the path. In the jargon of MANET we denote by the link stability, the durability and the lifetime of the link. Several protocols have been proposed to contribute for solving this problem. In this paper, we present a survey of recent routing solutions. We start by giving general definitions related to the mobility and the link stability. Then, we propose a classification for the routing protocols based on the link stability. For each proposed class, we will list examples of routing protocols. Finally, a conclusion and future research directions are discussed.

In this paper we study a prey–predator system in a variable environment. We show that seasonal variation of water level has a strong impact on persistence or extinction of fish populations living in an artificial lake. We also, give sufficient conditions for the existence of a periodic solution. Examples together with their numeric simulations show the feasibility of the main results.

Outcomes of interspecific competition, and especially the possibility of coexistence, have been extensively studied in theoretical ecology because of their implications in community assemblages. During the last decades, the influence of different time scales through the local/regional dynamics of animal communities has received an increasing attention. Nevertheless, different time scales involved in interspecific competition can result form other processes than spatial dynamics. Here, we envision and analyze a new theoretical framework that couples a game theory approach for competition with a demographic model. We take advantage of these two time scales to derive a reduced model governing the total densities of the two populations and we study how these two time scales interfere and influence outcomes of species competition. We find that a competition process occurring on a faster time scale than demography yields a ''priority effect'' where the first species introduced outcompetes the other one. We then confirm previous findings stipu- lating that species coexistence is favored by large difference in time scales because the extinction/recolonization process. Our results then highlight that an integration of demographic and competition time scales at both local and regional levels is mandatory to explain communities assemblages and should become a research priority.

In this paper, we propose a new mechanism to establish stable and sustainable paths between all pairs of nodes in a Mobile Ad hoc Network. In this mechanism, we use a stability function as the main path selection criterion based on the calculation of the mobility degree of a node relative to its neighbor. We applied this mechanism on the OLSR protocol (Optimized Link State Routing Protocol) to elect stable and sustainable MPR (Multipoint relays) nodes and topology. This mechanism significantly minimizes the recalculation of MPR and the routing tables recalculation process. Moreover, it guarantees other QoS (Quality of Service) metrics such as the packet loss and the response time. The simulation results show the effectiveness of our mechanism and encourage further investigations to extend it in order to guarantee other QoS requirements.

MANET networks (Mobile Ad hoc Networks) are a sub class of mobile and wireless networks. In this type of network, all the nodes are mobile and no fixed infrastructures are considered existing. Among the challenges of the MANET, the stability and the durability of the selected paths in the network. In a previous work, we proposed a solution to this challenge by taking into account the mobility of nodes. In this paper, we present an extension of this work by taking into account conjointly two metrics: the nodes' mobility and the residual energy. The validation results of this new work, using the OPNET simulator, have shown considerable improvement in the quality of installed paths compared to our previous work.

Water level may influence local community dynamics. We examine how seasonal variations in water level affect the outcome of prey-predator interactions in Parloup Lake in the south of France. We propose a new model to describe the annual cycle of persistence by using continuation theorem of coincidence degree.

We present a mathematical model of artificial pelagic multisite fisheries. The model is a stock–effort dynamical model of a fishery subdivided into artificial fishing sites such as fish-aggregating devices (FADs) or artificial habitats (AHs). The objective of the work is to investigate the effects of the number of sites on the global activity of the fishery. We consider a linear chain of fishing sites in which fish are harvested by fishing vessels and a free stock that is unattached to the sites and not exploited. Fish movements between the sites and the free stock, as well as vessel displacements between the sites, are assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and the total fishing effort. We show that there exists an optimal number of fishing sites that maximizes the total catch at equilibrium. We finally extend the model to the situation in which both fish attached to the sites and fish in the free stock are exploited.