Abstract In natural resource management, decision-makers often aim at maintaining the state of the system within a desirable set for all times. For instance, fisheries management procedures include keeping the spawning stock biomass over a critical threshold. Another example is given by the peak control of an epidemic outbreak that encompasses maintaining the number 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 viability kernel. We introduce the notion of conic quasimonotonicity reducibility. With this property, we provide a comparison theorem by inclusion between two viability kernels, corresponding to two control systems in the infinite horizon case. We also derive conditions for equality. We illustrate the method with a model for the biocontrol of a vector-transmitted epidemic.

中文翻译：

---

通过圆锥预序计算生存力核的比较定理

摘要 在自然资源管理中，决策者的目标通常是将系统状态始终保持在理想的范围内。例如，渔业管理程序包括将产卵种群生物量保持在临界阈值以上。另一个例子是流行病爆发的高峰控制，包括将感染人数保持在医疗能力以下。用数学术语来说，一个人控制一个动力系统。然后，当初始状态属于所谓的可行性内核时，将系统的状态始终保持在一个理想的集合内是可能的。我们引入了圆锥拟单调性可约性的概念。有了这个特性，我们通过包含两个可行性内核来提供一个比较定理，对应于无限地平线情况下的两个控制系统。我们还推导出平等的条件。我们用一个媒介传播流行病的生物控制模型来说明该方法。