The reproductive value in distributed optimal control models.
We show that in a large class of distributed optimal control models (DOCM), where population is described by a McKendrick type equation with an endogenous number of newborns, the reproductive value of Fisher shows up as part of the shadow price of the population. Depending on the objective function, the reproductive value may be negative. Moreover, we show results of the reproductive value for changing vital rates. To motivate and demonstrate the general framework, we provide examples in health economics, epidemiology, and population biology.
Wrzaczek
Stefan
S
Vienna University of Technology, Institute of Mathematical Methods in Economics (research group on Operations Research and Control Systems), Austria. wrzaczek@server.eos.tuwien.ac.at <wrzaczek@server.eos.tuwien.ac.at>
Kuhn
Michael
M
Prskawetz
Alexia
A
Feichtinger
Gustav
G
D000818:Animals; D015658:HIV Infections / Q000453:epidemiology / Q000517:prevention & control; D006801:Humans; D007231:Infant, Newborn; D008962:Models, Theoretical; D011235:Predatory Behavior; D012098:Reproduction