Mathematical modeling of solid cancer growth with angiogenesis

We develop a simple mathematical model to describe the solid cancer growth dynamics inducing angiogenesis in the absence of cancer controlling mechanisms.The initial conditions supplied to the dynamical system consist of a perturbation in form of pulse: The origin of cancer cells from normal cells of an organ of human body. Thresholds of interacting parameters were obtained from the steady states analysis. The existence of two equilibrium points determine the strong dependency of dynamical trajectories on the initial conditions. The thresholds can be used to control cancer.Cancer can be settled in an organ if the following combination matches: better fitness of cancer cells, decrease in the efficiency of the repairing systems, increase in the capacity of sprouting from existing vascularization, and higher capacity of mounting up new vascularization. However, we show that cancer is rarely induced in organs (or tissues) displaying an efficient (numerically and functionally) reparative or regenerative mechanism.A total of 562, 875 cancer deaths were recorded in the United States in 2007, and it is estimated that approximately 570, 000 died from cancer in 2010. The overall estimate of approximately 1.53 million new cases does not include carcinoma in situ of any site except urinary bladder, nor does it include basal cell and squamous cell cancers of the skin. Greater than 2 million unreported cases of basal cell and squamous cell skin cancer, approximately 54, 010 cases of breast carcinoma in situ, and 46, 770 cases of melanoma in situ are expected to be newly diagnosed in 2010 [1]. In the world, the estimate for 1990 suggested a total of 8.1 million new cases, divided almost exactly between developed and developing countries, and 5.2 million cancer deaths, about 55% of which occurred in developing countries [2].Cells of some organs, as the heart, stop proliferation after reaching their size, but others, like skin cells and cells that line body cavities, must proliferat