There are mathematical models that try to describe an evolution of cancer by considering an interaction of cancerous cells with healthy cells under the influence of various external and internal factors. These models are usually formulated as a set of ordinary nonlinear coupled differential equation, where the variables are either a concentration or number of various types of cells.
A well-known Gompertz law, for instance, describes the cell growth rate and is used as the basis in the problems discussed in this presentation. However, the main goal is not only modelling and predicting the cell population but also try to treat the cancer using a proper drug. Unfortunately, the drug very often not only influences or kills the malignant cells but also negatively impacts the population of healthy cells.
Thus, a problem of optimization have to be addressed to maximise the effect of the drug onto the cancerous cells and minimize its effect onto the healthy cells. The drug dosage and time intervals of the drug application are the main control parameter used in these studies, assuming the overall limited drug amount. In this presentation the mathematical models of the optimal control problems for 3 different types of cancer will be presented and results of the optimal treatment strategies will be demonstrated.
The University of NottinghamUniversity Park Nottingham, NG7 2RD
For all enquiries please visit: www.nottingham.ac.uk/enquire