Abstract
In this article, we intend to explore the role of using an ”infinite time horizon” framework to address the issues of sustainability and long-term strategies in the control of biological processes. We use two case study models to explain why considering a fixed or moving endpoint does not lead to the desired long-term effects. The first biological model considered concerns the spread of an infectious disease and its treatment as an infinite horizon optimal control problem. The second one deals with the metronomic chemotherapy cancer treatment over the remaining lifetime horizon of the patient. The latter is consistent with the conception of cancer as a chronic disease. Both models show structural differences in the choice of the objective functional, the first one uses a stabilization functional containing a weight function, the second one contains a damage functional which involves a density function.
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