Mathematical models of cancer fall into 2 classifications: molecular and macroscopic, with little integration between them, so far. Martin Nowak and co-workers have published a number of papers in PNAS and PLoS compbio in the former category that examine accumulation of driver and passenger mutations, waiting time, clonal expansion etc., all based on various standard probabilistic theories of branching and population (Moran, Wright-Fisher, etc). In terms of macroscopic theories, Robert Gatenby and colleagues have written numerous papers modeling cancer evolution, invasion, tumor-host interactions, etc. based on differential equations of the reaction-diffusion type (i.e. variations of the Lotka-Volterra equations). These papers, and subsequent ones that reference them, comprise much of the work that so far exists regarding mathematical descriptions of cancer. Hope that's helpful..
Mathematical models of cancer fall into 2 classifications: molecular and macroscopic, with little integration between them, so far. Martin Nowak and co-workers have published a number of papers in PNAS and PLoS compbio in the former category that examine accumulation of driver and passenger mutations, waiting time, clonal expansion etc., all based on various standard probabilistic theories of branching and population (Moran, Wright-Fisher, etc). In terms of macroscopic theories, Robert Gatenby and colleagues have written numerous papers modeling cancer evolution, invasion, tumor-host interactions, etc. based on differential equations of the reaction-diffusion type (i.e. variations of the Lotka-Volterra equations). These papers, and subsequent ones that reference them, comprise much of the work that so far exists regarding mathematical descriptions of cancer. Hope that's helpful..
Cells in the system of multicelular organism from positions of non-linear dynamics
V. A. Kotolupov, V. V. Isaeva
To get an overview, it may be worth checking "Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer" (Avner Friedman).
http://books.google.de/books/about/Tutorials_in_Mathematical_Biosciences_II.html?id=oC7_ZRqWK7IC&redir_esc=y
I believe there are certain models, perhaps too incipient, related to modelation via asymptotic homogenization method, there are also studies developed mainly in Santiago de Cuba, in Cuba, that are in test phase right now, you can try and chack this out
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