Optimal harvesting and optimal vaccination.
Two optimization problems are considered: Harvesting from a structured population with maximal gain subject to the condition of non-extinction, and vaccinating a population with prescribed reduction of the reproduction number of the disease at minimal costs. It is shown that these problems have a similar structure and can be treated by the same mathematical approach. The optimal solutions have a 'two-window' structure: Optimal harvesting and vaccination strategies or policies are concentrated on one or two preferred age classes. The results are first shown for a linear age structure problem and for an epidemic situation at the uninfected state (minimize costs for a given reduction of the reproduction number) and then extended to populations structured by size, to harvesting at Gurtin-MacCamy equilibria and to vaccination at infected equilibria.
Hadeler
K P
KP
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA. k.p.hadeler@uni-tuebingen.de
Müller
J
J
D017677:Age Distribution; D000367:Age Factors; D000465:Algorithms; D003140:Communicable Disease Control / Q000379:methods; D003141:Communicable Diseases / Q000276:immunology / Q000635:transmission; D006801:Humans; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011158:Population Growth; D014611:Vaccination / Q000191:economics / Q000379:methods*