Optimal control of age-structured population dynamics for spread of universally fatal diseases

Abstract

This article is concerned with the optimal control problem of age-structured population dynamics for the spread of universally fatal diseases. The existence and uniqueness of solution of the system, which consists of a group of partial differential equations with nonlocal boundary conditions, is proved. The Dubovitskii and Milyutin functional analytical approach is adopted in the investigation of the Pontryagin maximum principle of the system. The necessary condition is presented for the optimal control problem in fixed final horizon case. Finally, a remark on how to utilize the obtained results is also made.

Keywords:

• optimal control
• maximum principle
• necessary condition
• age-structured population dynamics

AMS Subject Classifications::

• 49B22
• 49K20
• 93C20

This article is related to:

Optimal control of age-structured population dynamics for spread of universally fatal diseases II

Acknowledgements

The authors appreciate the suggestions and comments presented by the editor and the anonymous reviewers, which have greatly improved this work. This work was supported in part by the National Natural Science Foundation of China under Grant 11001012 and 11171011, in part by the Excellent Young Scholars Research Fund of Beijing Institute of Technology (Expansion Programme, Category A), under Grant 2010CX04050, and in part by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality under Grant PHR20110820.