Abstract
In ChapterĀ 2 we considered the chemostat model and used mathematics to answer the question: How should we choose the outflow rate in order to harvest the maximum amount of bacteria. Our model however was incomplete because we assumed that the nutrient concentration in the growth chamber is constant in time, and hence our answer is questionable. In the present chapter we want to correct the answer, by basing it on a more complete mathematical model of the chemostat.
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References
Coddington, E.A.: An Introduction to Ordinary Differential Equations. Dover, New York (1989)
Butcher, J.C.: Numerical Methods for Ordinary Differential Equation. Wiley, New York (2008)
Strang, G.: Linear Algebra and Its Applications, 4th edn. Brooks/Cole, Belmont (2005)
Gantmacher, F.R.: The Theory of Matrices, vol. 2. Chelsea, New York (1959)
van den Driessche, P., Watmough, J.: Further notes on the basic reproduction number. In:Ā Mathematical Epidemiology, pp. 159ā178. Springer, Berlin/Heidelberg (2008)
Hale, J.K., Kocak, H.: Dynamics and Bifurcations. Springer, New York (1991)
Friedman, A., Hao, W., Hu, B.: A free boundary problem for steady small plaques in the artery and their stability. J. Diff. Eqs. 259, 1227ā1255 (2015)
Louzoun, Y., Xue, C., Lesinski, G.B., Friedman, A.: A mathematical model for pancreatic cancer growth and treatment. J. Theor. Biol. 351, 74ā82 (2014)
Friedman, A., Tian, J.P., Fulci, G., Chiocca, E.A., Wang, J.: Glioma virotherapy: the effects of innate immune suppression and increased viral replication capacity. Cancer Res. 66, 2314ā2319 (2006)
Day, J., Friedman, A., Schlesinger, L.S.: Modeling the immune rheostat of macrophages in the lung in response to infection. Proc. Natl. Acad. Sci. USA 106, 11246ā11251 (2009)
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Chou, CS., Friedman, A. (2016). The Chemostat Model Revisited. In: Introduction to Mathematical Biology. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-29638-8_8
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DOI: https://doi.org/10.1007/978-3-319-29638-8_8
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