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We present a mathematical model describing the time development of apopulation of tumors subject to mutual angiogenic inhibitory signaling. Basedon biophysical derivations, it describes organism-scale population dynamicsunder the influence of three processes: birth (dissemination of secondarytumors), growth and inhibition (through angiogenesis). The resulting model is anonlinear partial differential transport equation with nonlocal boundarycondition. The nonlinearity stands in the velocity through a nonlocal quantityof the model (the total metastatic volume). The asymptotic behavior of themodel is numerically investigated and reveals interesting dynamics ranging fromconvergence to a steady state to bounded non-periodic or periodic behaviors,possibly with complex repeated patterns. Numerical simulations are performedwith the intent to theoretically study the relative impact of potentiation orimpairment of each process of the birth/growth/inhibition balance. Biologicalinsights on possible implications for the phenomenon of "cancer withoutdisease" are also discussed.

A mathematical model of systemic inhibition of angiogenesis in metastatic development