Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Powiadomienia systemowe

Sesja wygasła!

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: model maltuzjański

Sortuj według:

Ogranicz wyniki do:

On population dynamics with campaign on contraception as control strategy

Ekhosuehi V. U., Chete F. O.

Journal of Mathematics and Applications

2018

Vol. 41

63--79

This work considers a population divided into two groups according to the adoption of contraception. The campaign in favour of contraception is modelled as a bounded optimal control problem within the framework of the logistic and the Malthusian models of population dynamics. The control is the fraction of non-adopters successfully educated on contraception. The objective is to maximise the number of non-adopters successfully educated on contraception over time. The optimisation problem is solved using the Pontryagin's maximum principle and the parameters of the model are estimated using the method of least squares.

Optimal strategy in chemotherapy for Malthusian model of cancer growth

Maroński R.

Acta of Bioengineering and Biomechanics

2017

Vol. 19, no. 1

63--68

Purpose: The problem of optimal strategy in cancer chemotherapy is reconsidered. Two incompatible goals should be completed: the number of cancer cells in the patient’s body should be reduced and the toxic effect of the therapy should be minimized. Such problem may be formulated in optimal control. The control function is the amount of the drug administered in the time unit. Methods: The Malthusian model of cell population growth is employed where the rate of increase of the number of cancer cells is proportional to the number of cells in population and an intrinsic rate that usually is assumed to be constant. The performance index is the amount of the drug cumulated in the patient’s body and it is minimized. A non-standard method of optimal control is used – method of Miele. Results: The optimal solutions are obtained for three cases: constant intrinsic rate, monotonically increasing/decreasing intrinsic rate and for periodic intrinsic rate. The optimal control is ununique for the first case – the result is irrespective of the strategy. Such result has been known earlier. The optimal control is unique for other cases and it is of bang-bang type. Conclusions: The ununique solution for constant intrinsic rate is surprising, therefore a mechanical analogy is given. The optimal strategy is in accordance with clinical experience for decreasing intrinsic rate. The optimal control is a periodic function of time for the intrinsic rate of sin/cos type – the drug should be administered, as its value is relatively high.