Modeling and migration-based control of depopulation

Area of Science:

• Mathematical modeling and control theory
• Population dynamics and spatial demography

Background:

• Habitats face population decline due to aging populations and significant migration outflows.
• Existing models may not fully capture the complex interplay of factors leading to depopulation.

Purpose of the Study:

• To develop a control-oriented population dynamics model addressing depopulation.
• To formulate controllability conditions and design a control strategy to prevent habitat depopulation.

Main Methods:

• A non-homogeneous ordinary differential equation model incorporating aging, migration costs, and carrying capacity.
• Analysis of spatial interaction-driven migration flows and their impact on population size.
• Development of a control strategy manipulating migration costs based on population size measurements.

Main Results:

• The proposed model effectively captures depopulation dynamics influenced by aging and migration.
• Controllability conditions were established for the population dynamics model.
• Simulation results demonstrate the effectiveness of the migration cost control strategy in preventing depopulation.

Conclusions:

• The developed mathematical model provides a robust framework for analyzing population dynamics in shrinking habitats.
• The proposed control strategy offers a viable method to mitigate depopulation by managing migration costs.
• The study highlights the importance of considering migration costs and aging in population management strategies.