SIR model with vaccination: bifurcation analysis

There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a SIR model where the class of Susceptible individuals grows logistically and has been subject to constant vaccination. We explicitly prove that the endemic equilibrium is a codimension two singularity in the parameter space $(\mathcal{R}_0, p)$, where $\mathcal{R}_0$ is the basic reproduction number and $p$ is the proportion of Susceptible individuals successfully vaccinated at birth. We exhibit explicitly the Hopf, transcritical, Belyakov, heteroclinic and saddle-node bifurcation curves unfolding the singularity. The two parameters $(\mathcal{R}_0, p)$ are written in a useful way to evaluate the proportion of vaccinated individuals necessary to eliminate the disease and to conclude how the vaccination may affect the outcome of the epidemic. We also exhibit the region in the parameter space where the disease persists and we illustrate our main result with numerical simulations, emphasizing the role of the parameters

Pulse vaccination in a modified SIR model: global dynamics, bifurcations and seasonality

We analyze a periodically-forced dynamical system inspired by the SIR model with pulse vaccination. We fully characterize its dynamics according to the proportion $p$ of vaccinated individuals and the time $T$ between doses. If the basic reproduction number is less than 1 (i.e. $\mathcal{R}_p<1$), then we obtain precise conditions for the existence and global stability of a disease-free $T$-periodic solution. Otherwise, if $\mathcal{R}_p>1$, then a globally stable $T$-periodic solution emerges with positive coordinates. We draw a bifurcation diagram $(T,p)$ and we describe the associated bifurcations. We also find analytically and numerically chaotic dynamics by adding seasonality to the disease transmission rate. In a realistic context, low vaccination coverage and intense seasonality may result in unpredictable dynamics. Previous experiments have suggested chaos in periodically-forced biological impulsive models, but no analytic proof has been given

Seasonal changes in a sandy beach fish assemblage at Canto Grande, Santa Catarina, South Brazil

Copyright © 2004 Coastal Education and Research Foundation (CERF).Neste trabalho realizaramse amostragens, com uma rede de praia, de modo a estudar a comunidade de peixes de substrato arenoso na enseada de Canto Grande, Santa Catarina, Brasil. As amostragens realizaramse em intervalos de 3 horas durante períodos de 24 h, numa base bimensal, entre Abril de 1996 e Fevereiro de 1997. Verificouse existir uma variação sazonal no número de espécies, densidade de peixes e biomassa, tendo os valores mais elevados ocorrido em Fevereiro (38 espécies, 257.6 peixes 1000 mˉ², 2286.4 g 1000 mˉ²). Recolheuse um total de 67 espécies, pertencentes a 56 géneros e a 33 famílias, sendo a comunidade dominada por sete espécies pertencentes a três famílias: Atherinella brasiliensis (Atherinidae); Brevoortia pectinata, Harengula clupeola e Sardinella brasiliensis (Clupeidae); Anchoviella lepidontostole, Cetengraulis edentulus e Lycengraulis grossidens (Engraulidae). Tanto a diversidade de espécies (H′) como a equitabilidade (J′) foram médias a elevadas ao longo do ano devido à baixa dominância. A maior mudança na estrutura da comunidade ocorreu entre os meses de Inverno (Julho e Agosto) e as outras estações. Nenhuma das espécies dominantes pode ser classificada como residente. Os principais predadores foram Pomatomus saltator (Inverno) e Trichiurus lepturus (Verão). A maior parte das espécies observadas foram ou peixes juvenis ou espécies pelágicas de pequeno tamanho e fortemente gregárias.ABSTRACT: A shallow-water fish assemblage, over a soft, sandy bottom, at Canto Grande, Santa Catarina, Brazil, was sampled with a beach seine. Sampling was undertaken at 3 h intervals over 24 h on a bimonthly basis between April 1996 and February 1997. There was a seasonal variation in the number of species, density of fishes and biomass with the highest values in February (38 species, 257.6 fish 1000 mˉ², 2286.4 g 1000 mˉ²). A total of 67 species, belonging to 56 genera and 33 families were collected and the assemblage was dominated by seven species belonging to three families: Atherinella brasiliensis (Atherinidae); Brevoortia pectinata, Harengula clupeola and Sardinella brasiliensis (Clupeidae); Anchoviella lepidontostole, Cetengraulis edentulus and Lycengraulis grossidens (Engraulidae). Species diversity (H′) and equitability (J′) were medium to high throughout the year due to the low dominance. The largest change in the assemblage structure occurred between winter months (July and August) and the other seasons. None of the dominant species can be classified as a resident. Main predators were Pomatomus saltator (winter) and Trichiurus lepturus (summer). Most of the species observed were either juvenile fish or small pelagic and strongly gregarious species

A following association between juvenile Epinephelus marginatus (Serranidae) and Myrichthys ocellatus (Ophichthidae)

Copyright © 2006 Société Française d’Ichtyologie.Une association entre un mérou noir juvénile Epinephelus marginatus (Serranidae) et Myrichthys ocellatus (Ophichthidae). Les informations sur le comportement des poissons marins du Brésil sont très réduites. Nous présentons dans ce travail la première observation d’une interaction dans laquelle un mérou noir Epinephelus marginatus (Lowe, 1834) agit comme suiveur d’un Myrichthys ocellatus (Lesueur, 1825). Ce comportement a été observé par hasard dans un récif de la Réserve marine biologique de Arvoredo, située sur la côte centrale de l’état de Santa Catarina, Brésil. Bien que l’observation ait été unique, l’interaction entre ces deux espèces nous a semblé apporter un bénéfice pour le mérou suiveur, qui peut ainsi chasser des proies cachées. Nous l’avons vu défendre activement sa place auprès de M. ocellatus, contre l’approche de deux autres jeunes mérous

First record of Darwin’s Slimehead, Gephyroberyx darwinii (Johnson, 1866) (Beryciformes: Trachichthyidae), in association with Brazilian deep reefs

Copyright © 2004 aqua, International Journal of Ichthyology.Três espécies da família Trachichthyidae ocorrem no sul do Brasil: Paratrachichthys atlanticus, Hoplostethus occidentalis e Gephyroberyx darwinii. Esta última é uma espécie que atinge tamanhos da ordem dos 600 mm (CT), vive na província bentopelágica até profundidades de 1210 metros. É encontrada em águas subtropicais distribuindo-se entre os paralelos 43ºN e 35ºS, sendo utilizada como fonte de alimento no leste do Atlântico central. O presente trabalho reporta a ocorrência de Gephyroberyx darwinii na costa brasileira entre as localidades de Vila Velha (ES) e Rio Grande (RS), em áreas de plataforma externa e talude superior, com profundidades variando de 70 a 520 metros. Suas ocorrências nestas áreas estiveram relacionadas a lances de pesca (onde Lophius gastrophysus é espécie alvo) sobre formações de corais vivos. Dados biométricos e merísticos de três espécimes são apresentados no trabalho.ABSTRACT: Three species of the Trachichthyidae family occur in the south of Brazil: Paratrachichthys atlanticus, Hoplostethus occidentalis and Gephyroberyx darwinii. G. darwinii may attain a length of 600 mm (TL). This benthopelagic species occurs at depths down to 1210 m and is generally found in subtropical waters between 43ºN and 35ºS. It is commercially exploited in the east central Atlantic for food and for oil. In this paper we report the occurrence of G. darwinii off the south and south-east coasts of Brazil between Vila Velha (Espírito Santo State) and Rio Grande (Rio Grande do Sul State), in outer shelf and slope areas, at depths between 70 and 520 m. In Brazil the trachichthyids were usually caught while fishing for Lophius gastrophysus over deep coral bottoms. Meristic and biometric data are presented for the three collected specimens

Habitat use by the juvenile dusky grouper Epinephelus marginatus and its relative abundance, in Santa Catarina, Brazil

Copyright © 2003 aqua, International Journal of Ichthyology.The dusky grouper (Epinephelus marginatus) is a species whose stock management deserves special attention. It has an important role in hard-bottom ecosystems and, as a protogynous hermaphrodite; it is especially susceptible to overfishing. Data on the species’ use of habitat, and on the way environmental and behaviour parameters influence its abundance can help to improve management and conservation strategies. The aim of this study was to evaluate the influence of bottom type, temperature and species behaviour on the abundance of E. marginatus, using a quadrate for visual census. An area of 80 mq., divided between rocky shore, rocky outcrop and sandy habitats was surveyed monthly. Densities of juveniles were: 1.16 groupers mˉ² over the rocky shore and 1.47 groupers mˉ² over the rocky outcrop, while no groupers were found over sand. Analysis of the yearly variation in abundance revealed a migratory pattern of dispersal and gathering. All size groups observed in this study were below the first maturation length.RÉSUMÉ: Le mérou Epinephelus marginatus est une espèce dont la gestion du stock réclame une attention spéciale. Son rôle est important dans les écosystèmes à fonds durs et en tant qu’hermaphrodite protogyne ; il est particulièrement sensible à la supêche. Des données sur l’utilisation de l’habitat par l’espèce et sur la façon dont les paramètres d’evironnement et de comportement déterminant sa fréquence peuvent aider à améliorer les stratégies de gestion et de préservation. L’objectif de cette étude consiste à évaluer l’impact di tye de substrat, de la température et du comportement de l’espèce sur l’abondance de E. margiantus, à l’aide d’un quadrat de recensement visuel. Une surface de 80m², composée de littoral rocheux, d’affleurements rocheux et d’habitats sableux, a été contrôlée mensuellement. Les densités de juvéniles étaient de: 1,16 mérous au mˉ² sur le littoral rocheux et de 1.47 au mˉ² sur les affleurements, alors qu’ils n’apparaissaient pas sur les fonds sableux. L’analyse de la variation annuelle en abondance a révélé un schéma migratoire de dispersion et de rassemblement. Tous les groupes observés dans cette étude avaient une taille inférieure à celle de la première maturation

Determination of the vertical dimension occlusion – case report

Abstract in proceedings of the Fourth International Congress of CiiEM: Health, Well-Being and Ageing in the 21st Century, held at Egas Moniz’ University Campus in Monte de Caparica, Almada, from 3–5 June 2019.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.info:eu-repo/semantics/publishedVersio

First record of Polyprion oxygeneios (Perciformes: Polyprionidae) for the southwest Atlantic Ocean and a northernmost range extension.

Copyright © 2004 The Fisheries Society of the British Isles.The hapuka Polyprion oxygeneios (Schneider & Foster) (Fig. 1) is an important deep-water commercial fish species, caught mainly off Australia, New Zealand, Juan Fernandez Archipelago off Chile, the Tristan da Cunha Group of the South Atlantic (Sepúlveda & Pequeño, 1986; May & Maxwell, 1986; Paulin et al., 1989; Paxton et al., 1989; Andrew et al., 1995) and incidentally caught off Chilean Patagonia (Nakamura et al., 1986). The distribution of P. oxygeneios is exclusively southern circum-global, intemperate-cold waters from 28_ to 43_ S (Paxton et al., 1989). Polyprion oxygeneios (Polyprionidae; Nelson, 1994) is mainly a demersal species with a depth range of 50–450 m, occurring over ‘rough’ ground from the central shelf to the upper slope (Paxton et al., 1989). It reaches 150 cm total length (LT) and may weigh up to 100 kg, its juveniles being found near the surface, probably associated with drifting material in a way similar to that recorded for Polyprion americanus (Bloch & Schneider) (Paxton et al., 1989; Saldanha, 1995). This paper reports the first record of P. oxygeneios from the south-west Atlantic