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Introduction to Mathematical Biology pp 75–85Cite as

General Systems of Differential Equations

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Abstract

In this chapter, we develop a theory for a system of differential equations that will be used to study models with many species.

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References

  1. Coddington, E.A.: An Introduction to Ordinary Differential Equations. Dover, New York (1989)

    MATH  Google Scholar 

  2. Butcher, J.C.: Numerical Methods for Ordinary Differential Equation. Wiley, New York (2008)

    Book  MATH  Google Scholar 

  3. Strang, G.: Linear Algebra and Its Applications, 4th edn. Brooks/Cole, Belmont (2005)

    MATH  Google Scholar 

  4. Gantmacher, F.R.: The Theory of Matrices, vol. 2. Chelsea, New York (1959)

    MATH  Google Scholar 

  5. van den Driessche, P., Watmough, J.: Further notes on the basic reproduction number. In: Mathematical Epidemiology, pp. 159–178. Springer, Berlin/Heidelberg (2008)

    Google Scholar 

  6. Hale, J.K., Kocak, H.: Dynamics and Bifurcations. Springer, New York (1991)

    Book  MATH  Google Scholar 

  7. Friedman, A., Hao, W., Hu, B.: A free boundary problem for steady small plaques in the artery and their stability. J. Diff. Eqs. 259, 1227–1255 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Louzoun, Y., Xue, C., Lesinski, G.B., Friedman, A.: A mathematical model for pancreatic cancer growth and treatment. J. Theor. Biol. 351, 74–82 (2014)

    Article  MathSciNet  Google Scholar 

  9. 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, 2314–2319 (2006)

    Article  Google Scholar 

  10. 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, 11246–11251 (2009)

    Article  Google Scholar 

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Authors and Affiliations

  1. Ohio State University, Columbus, Ohio, USA

    Ching-Shan Chou & Avner Friedman

Authors
  1. Ching-Shan Chou
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  2. Avner Friedman
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7.1 Electronic Supplementary Material

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Chou, CS., Friedman, A. (2016). General Systems of Differential Equations. In: Introduction to Mathematical Biology. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-29638-8_7

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