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C. Simon, B. Skritek, V.M. Veliov:
"Optimal immigration age-patterns in populations of fixed size";
Journal of Mathematical Analysis and Applications, 405 (2013), 1; S. 71 - 89.

Due to a low birth rate many countries need immigration to sustain a given population size. The resulting model consists of specific non-standard age-structured control systems on an infinite horizon. This paper investigates the question of optimal choice of the immigration age-profile within certain bounds. The main qualitative result is that under certain conditions the optimal control (the immigration age-profile) is time-invariant, although a dynamic framework is used. This makes it possible to give a detailed description of the optimal immigration policy and to obtain numerical solutions for the Austrian case. The analysis requires a number of new results obtained in the paper: a new type of transversality condition for the adjoint equation involved in the optimality conditions, generic conditions for well-posedness of the problem and appropriate stability conditions.

Optimal control; Age-structured system; Maximum principle; Population dynamics

http://dx.doi.org/10.1016/j.jmaa.2013.03.061

http://publik.tuwien.ac.at/files/PubDat_221992.pdf