Mathematical Modeling of the Darwinian Dynamics and the Immune Response to Cancer Evolution
Abstract
In this work, we build upon our previous works in \cite{[BDK13], [ABMC14]} to derive a new mathematical model of
the onset and evolution of cancer contrasted by the immune cells, using the approach of the kinetic theory of active particles as detailed in \cite{[BEAA15]}.
We present a qualitative analysis of the initial value problem and perform numerical simulations to show how some critical parameters affect the dynamics of the proposed model.
References
bibitem{[BEAA15]} N. Bellomo , A. Elaiw , A.M. Althiabi , M.A. Alghamdi, On the interplay between mathematics and biology: Hallmarks toward a new systems biology, Physics of Life Reviews, {bf 12}, 44-64, March (2015).
bibitem{[BDK13]} A. Bellouquid, E. De Angelis and D. Knopoff, From the modeling of the immune hallmarks of cancer to a black swan in biology, textit{Math. Models Methods Appl. Sci.}, {bf 23} 949--978, (2013).
bibitem{[ABMC14]} A. Bellouquid, and M. CH-Chaoui, Asymptotic analysis of a nonlinear integro-differential system modeling the immune response, emph{Comput Math Appl,} 68, 905-914, (2014).
