Mathematical Modeling of Biological Processes by Avner Friedman, Chiu-Yen Kao PDF
By Avner Friedman, Chiu-Yen Kao
This booklet on mathematical modeling of organic procedures incorporates a wide array of organic issues that exhibit the facility of arithmetic and computational codes in constructing organic procedures with a rigorous and predictive framework. issues comprise: enzyme dynamics, unfold of ailment, harvesting micro organism, pageant between dwell species, neuronal oscillations, delivery of neurofilaments in axon, melanoma and melanoma treatment, and granulomas. entire with an outline of the organic historical past and organic query that calls for using arithmetic, this ebook is built for graduate scholars and complicated undergraduate scholars with in simple terms uncomplicated wisdom of standard differential equations and partial differential equations; heritage in biology isn't really required. scholars will achieve wisdom on how one can software with MATLAB with out earlier programming event and the way to exploit codes with the intention to try out organic hypothesis.
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Extra info for Mathematical Modeling of Biological Processes
If p is then decreased, the system remains in low activation until p crosses the lower critical value p1 , at which time the system bounces back to the high activation state. Thus for p1 < p < p2 the system can be in either state, depending on its recent history. Mathematical models of hysteresis may help understand how more complex systems with hysteretic components work. © Springer International Publishing Switzerland 2014 A. -Y. 1007/978-3-319-08314-8_6 61 62 6. BIFURCATION THEORY We consider bifurcation theory for a system of diﬀerential equations with bifurcation parameter p: dx = f (x, p).
Epidemiologists gather data and apply a broad range of biomedical and psychosocial theories to generate theory, test hypotheses, and make educated, informed assertions as to which relationships are causal and in which way. For example, many epidemiological studies are aimed at revealing unbiased relationships between exposure to smoking, biological agents, stress, or chemicals to mortality and morbidity. In the identiﬁcation of causal relationship between these exposures and outcome epidemiologists use statistical and mathematical tools.
Relation dx dy dz + + = 0 or x + y + z = const. = A dt dt dt can be viewed as conservation of the total nitrogen mass. The steady point (x0 , y0 , z0 ) where all three species exist is (x0 , y0 , z0 ) = γA α−β β γ + , , γ+δ γ+δ δ γ+δ A− The α β − γ δ provided α β β−α , A> + . 1) γ+δ γ δ We observe that whereas α and β are predetermined by the physiology of the planktons, the rates γ and δ depend on the consumption eﬃciency of the phytoplankton and zooplankton. 1) holds, then (x0 , y0 , z0 ) exists as a steady state.
Mathematical Modeling of Biological Processes by Avner Friedman, Chiu-Yen Kao