  In natural resource management, decision-makers often aim at maintaining
thestate of the system within a desirable set for all times.For instance,
fisheries management procedures include keeping thespawning stock biomass over
a critical threshold.Another example is given by the peak control of an
epidemic outbreakthat encompasses maintaining thenumber of infected individuals
below medical treatment capacities.In mathematical terms, one controls a
dynamical system.Then, keeping the state of the system within a desirable set
for all times is possible when the initial state belongs to the so-called
viabilitykernel. We introduce the notion of conic quasimonotonicity
reducibility.With this property, we provide a comparison theorem by inclusion
between two viabilitykernels, corresponding to two control systems in the
infinite horizon case. Wealso derive conditions for equality. We illustrate the
method with a model for thebiocontrol of a vector-transmitted epidemic.
