This study is developed a mathematical model to describe interactions between tumor cells and a compliant blood vessel that supplies oxygen to the region. In addition to proliferating, it is assumed that the tumor cells die through apoptosis and necrosis. It is also assumed that pressure differences within the tumor mass, caused by spatial variations in proliferation and degradation, cause cell motion. The behavior of the blood vessel is coupled into the model for the oxygen tension. The model equations tracked the evolution of the densities of live and dead cells, the oxygen tension within the tumor, the live and dead cell speeds, the pressure and the width of the blood vessel. This study presented the exact solutions to the model for certain parameter regimes and then solve the model with artificial neural networks for more general parameter regimes. This study also showed the resulting steady-state and porous medium behavior varies as the time is changed.