Control of a general lethal growth process

Branching processes with random absorbing processes

“…(1) Let g: N°~ [1,00] and E(Z~IZ~>0) = mA(n)~g(n) for almost all n E N°(f.a.a.n E N°), i.e., for all but a finite number of exceptions.…”

“…If the exact efficiency of A is unknown, our results may be a little help, because we can estimate m; (n) by many observations under the same treatment and the same circumstances, and then choose A such that (a) L n cf>"mA(n) diverges, and (b) there is no (experimentally verified) weaker dose such that rnA (n) satisfies (a). (The case where the exact efficacy of the medicine are known is treated by Neuts [6] for a Yule process, and for more general processes by Cherniavsky and Taylor [1]. In addition they optimize the result of a treatment under the assumption that the impact of the treatment strategy and the harmful influence of the malignant population on the host are known too.…”

Some strategies for harvesting a single species

“…The problem of harvesting members of a biological species is of considerable interest in many areas of application. For example, one may be interested in culling from a population of microorganisms in a chemostat (D'Ans, Kokotovi5 and Gottlieb, 1971), controlling a lethal growth process (Cherniavsky and Taylor, 1972), or it may be desirable to destroy members of a bacterial population by the administration of a drug (Bellman and Kalaba, 1960), or one may seek to remove insect pests from damaging a crop (Becket, 1970;Shoemaker, 1973). A brief survey of some of the areas of biological control is given by Jaquette (1972).…”