Solution methods for age-structured optimal control models with feedback

Abstract

Modeling the dynamics of infectious diseases, illicit drug initiation, or other systems, where the age of an individual or the duration of being in a specific state is essential, leads to a generalized form of the McKendrick equations, i.e., a system of first-order partial differential equations in the time-age space. Typically such models include age-specific feedback components which are represented by integral terms in the right hand side of the equation. This paper presents the general framework of such optimal control models, the corresponding necessary optimality conditions and two different approaches for numerical solution methods. © Springer-Verlag 2004.