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### Open Access Journals

MBE

A replicator equation with explicit space and global regulation is considered. This model provides a natural
framework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable state are provided. A sufficient condition for a uniform stationary state to be a spatially distributed evolutionary stable state is presented and illustrated with examples.

MBE

In this work an optimization problem for a leukemia treatment model
based on the Gompertzian law of cell growth is considered. The quantities
of the leukemic and of the healthy cells at the end of the therapy are chosen
as the criterion of the treatment quality. In the case where the number of
healthy cells at the end of the therapy is higher than a chosen desired number,
an analytical solution of the optimization problem for a wide class of therapy
processes is given. If this is not the case, a control strategy called

*alternative*is suggested.
MBE

A mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. Additionally, we assume some phase constraints for the number of the malignant and the healthy cells and for the total dose of the drug during the whole treatment process.

We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy.

We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy.

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