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Optimal birth control of population dynamics.

W L Chan, B Z Guo

Journal of Mathematical Analysis and Applications

|November 1, 1989

Summary

This study develops optimal birth control strategies for structured populations using advanced mathematical techniques. The research focuses on time-optimal control problems within a distributed parameter system framework.

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Area of Science:

Mathematical Biology
Control Theory
Population Dynamics

Background:

McKendrick-type age-structured population models are complex distributed parameter systems.
Optimal control is crucial for managing population dynamics and resource allocation.
Nonlocal bilinear boundary control presents unique mathematical challenges.

Purpose of the Study:

To investigate optimal birth control policies for McKendrick-type populations.
To apply the functional analytic approach of Dubovitskii and Milyutin.
To develop maximum principles for time-optimal control problems with various conditions.

Main Methods:

Utilizing a functional analytic approach (Dubovitskii-Milyutin).
Developing maximum principles for partial differential equations with nonlocal boundary control.
Analyzing time-optimal control, target set problems, and infinite horizon cases.

Main Results:

Established maximum principles for optimal control problems in age-structured populations.
Investigated solutions for time-optimal control with free end conditions and fixed horizons.
Extended analysis to target set problems and infinite planning horizons.

Conclusions:

The functional analytic approach provides a robust framework for optimal control in structured populations.
Developed methodologies are applicable to complex population dynamics and resource management.
Further research can explore extensions to more intricate population models and control objectives.

Keywords:

Demographic Factors Models, Theoretical Policy Population Population Dynamics Population Policy Research Methodology Social Policy

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