  We present a mathematical model describing the time development of a
population of tumors subject to mutual angiogenic inhibitory signaling. Based
on biophysical derivations, it describes organism-scale population dynamics
under the influence of three processes: birth (dissemination of secondary
tumors), growth and inhibition (through angiogenesis). The resulting model is a
nonlinear partial differential transport equation with nonlocal boundary
condition. The nonlinearity stands in the velocity through a nonlocal quantity
of the model (the total metastatic volume). The asymptotic behavior of the
model is numerically investigated and reveals interesting dynamics ranging from
convergence to a steady state to bounded non-periodic or periodic behaviors,
possibly with complex repeated patterns. Numerical simulations are performed
with the intent to theoretically study the relative impact of potentiation or
impairment of each process of the birth/growth/inhibition balance. Biological
insights on possible implications for the phenomenon of "cancer without
disease" are also discussed.
