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Growth Models in Comparison

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Abstract

Growth processes are the basis of many models. In this paper the basic assumptions, which all types of growth models share, are introduced first. After that three types of growth models in the areas of epidemiology, computer science, and economics are represented. In the last section a type of models is characterized which has monotonic solutions only. Employing this knowledge some hints are derived how to build models admitting solutions with all kinds of nonmonotonic behaviour.

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References

  • BAILEY, N. T. J. (1975), The Mathematical Theory of Infectious Diseases and its Applications, Charles Griffin & Co. Ltd, London.

    Google Scholar 

  • FLECK, F. (1981), Regularities of Market Penetration Processes Caused by Individual Consumer Behaviour, Athenaeum; Cambrigde, Mass.: Oelgeschlager, Gunn and Hain.

    Google Scholar 

  • GLEIßNER, W. (1985), “Market Penetration and Optimal Prices, a Probabilistic Model using Nonstationary Markov Processes and Bellman’s Functional Equation to Determine an Optimal Price Policy” in Optimal Control Theory and Economic Analysis edited by G. Feichtinger, North Holland Publishing Company, 279–292.

    Google Scholar 

  • GLEIßNER, W. (1988), “The Spread of Epidemics”, Journal of Applied Mathematics and Computation 27 (2), 167–171.

    CrossRef  Google Scholar 

  • GLEIßNER, W. (1989), “A Mathematical Theory for the Spread of Computer Viruses”, Computers & Security 8 (1), 35–41.

    CrossRef  Google Scholar 

  • HALE, J. K. (1977), Theory of Functional Differential Equations, Springer-Verlag.

    Google Scholar 

  • LANG, S. (1972), Linear Algebra, Addison Wesley.

    Google Scholar 

  • MURRAY, J. D. (1989), Mathematical Biology, Springer-Verlag.

    Google Scholar 

  • NEUMANN, K. (1969), Dynamische Optimierung, BI-Verlag, Mannheim.

    Google Scholar 

  • SCHNEEWEIFI, CH. (1974), Dynamisches Programmieren, Physica-Verlag, Wurzburg — Wien.

    Google Scholar 

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© 1993 Springer-Verlag Berlin · Heidelberg

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Gleißner, W. (1993). Growth Models in Comparison. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78508-5_19

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  • DOI: https://doi.org/10.1007/978-3-642-78508-5_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78510-8

  • Online ISBN: 978-3-642-78508-5

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