Sustainable thresholds for cooperative epidemiological models

In this paper, we introduce a method for computing sustainable thresholds for controlled cooperative models described by a system of ordinary differential equations, a property shared by a wide class of compartmental models in epidemiology. The set of sustainable thresholds refers to constraints (e.g., maximal "allowable" number of human infections; maximal "affordable" budget for disease prevention, diagnosis and treatments; etc.), parameterized by thresholds, that can be sustained by applying an admissible control strategy starting at the given initial state and lasting the whole period of the control intervention. This set, determined by the initial state of the dynamical system, virtually provides useful information for more efficient (or cost-effective) decision-making by exhibiting the trade-offs between different types of constraints and allowing the user to assess future outcomes of control measures on transient behavior of the dynamical system. In order to accentuate the originality of our approach and to reveal its potential significance in real-life applications, we present an example relying on the 2013 dengue outbreak in Cali, Colombia, where we compute the set of sustainable thresholds (in terms of the maximal "affordable" budget and the maximal "allowable" levels of active infections among human and vector populations) that could be sustained during the epidemic outbreak.