We consider a class of biological networks where the nodes are associated with first-order linear dynamics and their interactions, which can be either activating or inhibitory, are modelled by nonlinear Michaelis–Menten functions (i.e., Hill functions with unitary Hill coefficient), possibly in the presence of external constant inputs. We show that all the systems belonging to this class admit at most one strictly positive equilibrium, which is stable; this property is structural, i.e., it holds for any possible choice of the parameter values, and topology-independent, i.e., it holds for any possible topology of the interaction network. When the network is strongly connected, the strictly positive equilibrium is the only equilibrium of the system if and only if the network includes either at least one inhibiting function, or a strictly positive external input (otherwise, the zero vector is an equilibrium). The proposed stability results hold also for more general classes of interaction functions, and even in the presence of arbitrary delays in the interactions.

While there is widespread concern regarding the impact of pesticides on honey bees, well-replicated field experiments, to date, have failed to provide clear insights on pesticide effects. Here, we adopt a systems biology approach to gain insights into the web of interactions amongst the factors influencing honey bee health. We put the focus on the properties of the system that depend upon its architecture and not on the strength, often unknown, of each single interaction. Then we test in vivo, on caged honey bees, the predictions derived from this modelling analysis. We show that the impact of toxic compounds on honey bee health can be shaped by the concurrent stressors affecting bees. We demonstrate that the immune-suppressive capacity of the widespread pathogen of bees, deformed wing virus, can introduce a critical positive feed-back loop in the system causing bistability, i.e., two stable equilibria. Therefore, honey bees under similar initial conditions can experience different consequences when exposed to the same stressor, including prolonged survival or premature death. The latter can generate an increased vulnerability of the hive to dwindling and collapse. Our conclusions reconcile contrasting field-testing outcomes and have important implications for the application of field studies to complex systems.