RESUMO
In this paper, we formulate a nonlinear system of difference equations that models the three-stage life cycle of the deer tick over four seasons. We study the effect of seasonality on the stability and oscillatory behavior of the tick population by comparing analytically the seasonal model with a non-seasonal one. The analysis of the models reveals the existence of two equilibrium points. We discuss the necessary and sufficient conditions for local asymptotic stability of the equilibria and analyze the boundedness and oscillatory behavior of the solutions. A main result of the mathematical analysis is that seasonality in the life cycle of the deer tick can have a positive effect, in the sense that it increases the stability of the system. It is also shown that for some combination of parameters within the stability region, perturbations will result in a return to the equilibrium through transient oscillations. The models are used to explore the biological consequences of parameter variations reflecting expected environmental changes.
Assuntos
Ixodes/crescimento & desenvolvimento , Modelos Biológicos , Estações do Ano , Algoritmos , Animais , Clima , Meio Ambiente , Estágios do Ciclo de Vida , Dinâmica não Linear , Densidade Demográfica , Dinâmica Populacional , Crescimento DemográficoRESUMO
A favorable effect of laser therapy in rheumatic diseases was demonstrated in a previous paper [9] but it was not possible to estimate whether this benefit was due to an antiinflammatory, analgesic or decontracturant effect. In this work the effect of laser therapy was tested on an experimental inflammation in rats. Laser irradiation reduced the volume of the inflammation during 6 days of treatment more than 85% and prevented the appearance of necrosis. In the control group, the reduction of inflammation was of only 22.86%, the difference vs. the treated group being significant for p = 0.00009, and eight rats of the ten developed local necrosis.
Assuntos
Inflamação/radioterapia , Terapia a Laser , Análise de Variância , Animais , Carragenina , Estudos de Avaliação como Assunto , Feminino , Membro Posterior , Inflamação/induzido quimicamente , Masculino , Ratos , Fatores de TempoRESUMO
The effect of a 940-980 nm length wave laser radiation in rheumatic degenerative diseases was studied in 136 patients unresponsive to or with contraindications for antiinflammatory non-steroid therapy. The evolution was clinically estimated using four parameters; pain, muscular contracture, local edema and the impairment of the articular mobility. All patients presented a beneficial evolution appearing gradually during the treatment. The osteoarthritis of the knee, ankle and shoulder evolved worse than the painful back. The painful back presented an improved evolution when it was located at the thoracal level. No adverse reaction was observed during this study.