In this paper a new mathematical model is developed for the dynamics between tumor cells, normal cells, immune cells, chemotherapy drug concentration and drug toxicity. Then, the theorem of Lyapunov stability is applied to design treatment strategies for drug protocols that ensure a desired rate of tumor cell kill and push the system to the area with smaller tumor cells. Using of this theorem a...

Mathematical models can simulate the growth and proliferation of cells in the interaction with healthy cells, the immune system and measure the toxicity of drug and its effects on healthy tissue pay. One of the main goals of modeling the structure and growth of cancer cells is to find a control model suitable for administration among patients. In this study, a new mathematical model is designed...

Mathematical modeling has recently been added as a tool in the fight against cancer. The field of mathematical oncology has received great attention and increased enormously, but over-optimistic estimations about its ability have created unrealistic expectations. We present a critical appraisal of the current state of mathematical models of cancer. Although the field is still expanding and usef...

determination of critical points on hot stress-strain curve of metals is crucial in thermo-mechanical processes design. in this investigation a mathematical modeling is given to illustrate the behavior of metal during hot deformation processes such as hot rolling. the critical strain for the onset of dynamic recrystallization has been obtained as a function of strain at the maximum stress. in a...