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Optimal chemical control of populations developing drug resistance. (English) Zbl 0779.92011
The paper analyses a system of differential equations for the control of the growth of certain populations by the use of chemical treatment. A class of optimal control problems with performance criterion depending on a parameter is formulated. Using Pontryagin’s minimum principle, it is proved that the optimal strategy is of the ‘bang-off’ type, being independent of the natural growth rates and the kill rates of drugs. The main theorem is then applied to the case of cycle nonspecific cancer chemotherapy and to the control of bacteria populations in cellulose media.
Reviewer: S.Curteanu (Iaşi)

92C50 Medical applications (general)
49N70 Differential games and control
49N75 Pursuit and evasion games
92C40 Biochemistry, molecular biology
92E20 Classical flows, reactions, etc. in chemistry
92D25 Population dynamics (general)