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Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies

Alexander Lorz, Tommaso Lorenzi, Michael E. Hochberg, Jean Clairambault, Benoît Perthame (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...

Positive solutions for a system of fractional boundary value problems

Henderson, Johnny, Luca, Rodica (2017)

Proceedings of Equadiff 14

We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.

Positive solutions of a renewal equation

Janusz Traple (1992)

Annales Polonici Mathematici

An existence theorem is proved for the scalar convolution type integral equation x ( t ) = - h ( t - s ) f ( s , x ( s ) ) d s .

Probability distribution solutions of a general linear equation of infinite order

Tomasz Kochanek, Janusz Morawiec (2009)

Annales Polonici Mathematici

Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation F ( x ) = Ω F ( τ ( x , ω ) ) P ( d ω ) in the class of probability distribution functions.

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