Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of mosquitoes carrying the Wolbachia parasite that need to be introduced into the natural population. The latter are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this paper, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then introduce a simple feedback control law to synthesize an introduction protocol, and prove that the population is guaranteed to converge to a stable equilibrium where the totality of mosquitoes carry Wolbachia. The techniques are based on the theory of monotone control systems, as developed after Angeli and Sontag. Due to bistability, the considered input-output system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.

Soil attributes and efficiency of sulfentrazone on control of purple nutsedge (Cyperus rotundus L.)

Herbicidas aplicados ao solo são submetidos à adsorção, lixiviação e degradação por processos físicos, químicos e biológicos, além da absorção pelas plantas. Todos esses processos são afetados pela classe dos solos onde foram aplicados e das condições climáticas reinantes logo após a aplicação, que afetarão a eficiência dos produtos no controle de plantas daninhas. Investigaram-se as influências dos atributos de solos e condições de cultivo na eficiência do herbicida sulfentrazone no controle da planta daninha tiririca (Cyperus rotundus L.). O Latossolo Vermelho-Amarelo Distrófico (LVAd), o Latossolo Vermelho (LVd - Distrófico; LVdf - Distroférrico; LVef - Eutroférrico) e o Nitossolo Vermelho Eutrófico (NVe) foram coletados sob duas condições de cultivo, visando obter solos com teores diferenciados de argila, óxido de ferro e matéria orgânica. As amostras dos solos foram submetidas à caracterização granulométrica, química e mineralógica e, em seguida, utilizadas no bioensaio de avaliação da eficiência do sulfentrazone (1,6 L p.c. ha-1) no controle da tiririca em condições de pré-emergência. O sulfentrazone apresentou comportamento diferenciado entre as classes de solos estudados e a sua eficiência diminuiu com o aumento do teor de óxido de ferro nos solos, na seguinte ordem: LVAd, LVd, NVe, LVef e LVdf, sendo que as variações nos teores de argila (240 a 640 g kg-1) e da matéria orgânica (12 a 78 g kg-1) dos solos não interferiram na eficiência do sulfentrazone.

Biological control of Bradysia matogrossensis (Diptera : Sciaridae) in mushroom cultivation with predatory mites

Larvae of Sciaridae flies (Diptera) cause considerable damage to the mushroom Agaricus blazei (Murrill) ss. Heinemann in Brazil. Brazilian growers have had considerable difficulties in controlling this pest. The objective of this work was to test the effect of the predatory Laelapidae mite Stratiolaelaps scimitus (Womersley) as a control agent of Bradysia matogrossensis (Lane) in cultures of A. blazei. The work corresponded to an evaluation of the efficiency of that predator when released in boxes containing each about 15 L of commercial mushroom compost naturally infested with the pest. The results showed a significant effect of that predator on the population of B. matogrossensis. The release of either 665 or 1330 S. scimitus per box significantly reduced the pest population to levels that, according to grower's experience, apparently could not cause considerable damage. The positive results obtained warrant the conduction of complementary studies to determine the lowest rates of the predator that could still produce acceptable levels of control.