Isoperimetric Control Inequality: Application to the Management of Limited Resources in Times of Pandemics

According to numerous past epidemic outbreaks, a poorly controlled pandemic can have catastrophic effects, killing millions of people in a matter of decades and having a significant effect on demography. When an unprecedented epidemic suddenly goes to the global level, it becomes more difficult to predict how the existing health and economic resources will succeed in managing the situation especially when the number of deceased people increases quasi-exponentially as happened during the COVID-19 time. In this chapter, we try to answer the question: how is it possible to devise the best metapopulation control management plans that take into account the many health resource constraints that decision-makers may encounter during pandemic emergencies? For that, we state in this chapter, the fundamental rules of optimal control strategies that are subject to multi-group-like models and which for the particularity of the topic, need in addition to relying on the frameworks of the recently devised multi-region control systems, the implementation of what we refer to isoperimetric control inequalities to make practical policies with the best administration of scarce resources. We provide different theoretical scenarios of this approach and a review analysis when it can be used in concrete examples as when considering dengue epidemic breakouts for a region within itself under budgetary restrictions on insecticide supply, or when addressing immunization-related shortages in two interconnected regions. In the end, we conclude that any control approach would be ineffective if the problems of the health system limitations and the lack of medical resources are not addressed.