RESUMO
In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the Wolbachia symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called principle of competitive exclusion. Using tools borrowed from monotone dynamical system theory, in the proposed model, we prove the existence of an invariant threshold manifold that allows us to provide practical recommendations for performing single and periodic releases of Wolbachia-carrying mosquitoes, seeking the eventual elimination of wild insects that are capable of transmitting infections to humans. We illustrate these findings with numerical simulations using parameter values corresponding to the wMelPop strain of Wolbachia that is considered the best virus blocker but induces fitness loss in its carriers. In these tests, we considered multiple scenarios contrasting a periodic release strategy against a strategy with a single inundative release, comparing their effectiveness. Our study is presented as an expository and mathematically accessible tool to study the use of Wolbachia-based biocontrol versus more complex models.
Assuntos
Aedes , Wolbachia , Animais , Humanos , Reprodução , Fertilidade , Dinâmica PopulacionalRESUMO
O objetivo do presente estudo centra-se em conhecer o modelo competitivo da distância percorrida por futebolistas na Uefa Euro 2008, mediante as posições de jogo, os tempos e a distância total percorrida durante as partidas. Foram analisadas todas as partidas das 16 seleções, totalizando 31 jogos, dos quais participaram 460 futebolistas. Posteriormente, produziram-se informações descritivas e inferenciais. Os principais resultados apontam que: i) futebolistas da elite europeia percorreram 10232 ± 852m; ii) meio-campistas (10894 ± 648m) percorreram maior distância, seguidos pelos laterais (10274±694m), atacantes (10108 ± 624m), zagueiros (9498 ± 592m) e goleiros (4198 ± 610m); iii) a distância média percorrida no 1º tempo (4907 ± 201m) das partidas foi maior do que a do 2º tempo (4890 ± 238m).
The aim of this study focuses on knowing the competitive model of distance covered by soccer players in the Uefa Euro 2008, in the positions of the game, times and the total distance covered during the matches. It was analyzed all matches from 16 teams, totaling 31 games of which involved 460 soccer players. Subsequently, produced descriptive and inferential information. The main results show that: i) European soccer players elite covered 10232 ± 852m; ii) a midfielders (10894 ± 648m) greater distance covered, followed by external defenders (10274 ± 694m), forwards (10108 ± 624m), central defenders (9498 ± 592m) and goalkeepers (4198 ± 610m); iii) the average of covered distance at first half (4907 ± 201m) for matches was higher than the second half (4890 ± 238m).
El objetivo de este estudio se centra en conocer el modelo competitivo de la distancia recorrida por futbolistas en Uefa Euro 2008, por las posiciones de juego, tiempos y la distancia total recorrida durante los partidos. Se analizaron todos los juegos de 16 selecciones, totalizando 31 juegos que participaron 460 futbolistas. Posteriormente, fueran producidas informaciones descriptivas e inferencia. Los principales resultados indican que: i) futbolistas de la elite Europea recorrerán 10232 ± 852m; ii) centro-campistas (10894 ± 648m) recorrerán mayor distancia, seguido por laterales (10274 ± 694m), delanteros (10108 ± 624m), defensores (9498 ± 592m) y porteros (4198 ± 610m); iii) la media distancia recorrida en lo 1º tiempo (4907 ± 201m) de los juegos fue superior a 2º tiempo (4890 ± 238m).