Optimal control and calibration modeling of forest regeneration under anthropogenic pressures: the day forest ecosystem (Djibouti)

Forest ecosystems in arid and semi-arid regions face increasing threats from climate change and human pressures, making active restoration strategies a scientific and policy priority. In these environments, plant–plant facilitation, particularly the nurse role of certain species is a key mechanism for sustaining endemic vegetation. This paper investigates the optimal control and calibration of a compartmental forest regeneration model, with Acacia seyal as the selected nurse species, applied to the day forest ecosystem (Djibouti), a semi-arid habitat harboring a major declining population of East African junipers ( Juniperus procera ). The model incorporates facilitative plant–plant interactions and two time-dependent control variables representing management interventions aimed at reducing human-induced disturbances. Optimal controls are characterized via Pontryagin’s Maximum Principle, and their existence and uniqueness are formally established. The model is then calibrated through a structured procedure grounded in field studies and ecosystem reports from the day forest. Numerical simulations are subsequently performed to evaluate a range of management and protection strategies under realistic conditions. Results show that simultaneously activating both human-disturbance reduction interventions yields the most effective restoration outcomes. These findings provide a replicable quantitative framework for designing cost-effective restoration policies in semi-arid ecosystems under human pressure, with direct applicability to comparable ecosystems across the Horn of Africa and beyond.