Effects of time lags on transient characteristics of a nutrient cycling model.

A simple ecosystem with limiting nutrient cycling is modeled by chemostat equations with an integral term describing the continuous time lag involved in the process of nutrient regeneration from organic sediments. The same model has already been proposed in a previous paper, where conditions for boundedness of the solutions and stability of the equilibria were given. This paper is concerned with the relationships between resilience, that is, the speed with which the system returns to a stable equilibrium following a perturbation, and the time lag in the nutrient recycling process. Simple algorithms are given for the numerical calculation of the characteristic return time toward the stable equilibrium following a small perturbation. These methods also allow us to distinguish the case of monotone convergence from that of oscillatory convergence toward equilibrium. The numerical results obtained show that the presence of the time lag causes both qualitative and quantitative modifications in the dependence of equilibrium resilience on some relevant ecological parameters, such as the input nutrient concentration and the recycling extent. Analytical results for "quasi-closed" ecosystems are given that show that such stable systems are characterized by a very low resilience.

Stability in chemostat equations with delayed nutrient recycling.

The growth of a species feeding on a limiting nutrient supplied at a constant rate is modelled by chemostat-type equations with a general nutrient uptake function and delayed nutrient recycling. Conditions for boundedness of the solutions and the existence of non-negative equilibria are given for the integrodifferential equations with distributed time lags. When the time lags are neglected conditions for the global stability of the positive equilibrium and for the extinction of the species are provided. The positive equilibrium continues to be locally stable when the time lag in recycling is considered and this is proved for a wide class of memory functions. Computer simulations suggest that even in this case the region of stability is very large, but the solutions tend to the equilibrium through oscillations.

A nonlinear three-compartment model for the administration of 2',3'-dideoxycytidine by using red blood cells as bioreactors.

A non-linear three-compartment model is proposed to describe a new strategy for the administration of 2',3'-dideoxycytidine (ddCyd) in the treatment of HIV infections. The drug is injected after having been encapsulated in a non-diffusible form (ddCMP) into erythrocytes. Numerical solutions show that by this treatment the highest ddCyd blood concentration is strongly reduced and in turn its toxicity, while long-lasting therapeutic effect is assured. The model is compared with experimental data in vitro.