Skip to main content
SpringerLink
Log in

A simple mathematical model of the thermal death of microorganisms

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

This note is concerned with a simple mathematical model of how a population of bacterial spores decrease with time when subjected to a uniform temperature. The model assumes that there is a Boltzman distribution of energy among water or other molecules surrounding the assumed single lethal target in a spore; it assumes that repair is not possible; and that only molecules with energies above a critical level cause inactivation. The model provides new insight concerning the ‘kill-rate’ of spores during ultra heat treatment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Abramowitz, M. and I. Stegun (Eds.) 1968. Handbook of Mathematical Functions. New York: Dover.

    Google Scholar 

  • Atwood, K. C. and A. Norman. 1949.Proc. Natn. Acad. U.S.A. 35, 696.

    Article  Google Scholar 

  • Casolari, A. 1981.J. theor. Biol. 88, 1.

    Article  Google Scholar 

  • Charm, S. E. 1958.Food Tech. 12, 4.

    Google Scholar 

  • Jordan, R. C. and G. E. Jacobs. 1944.J. Hyg., Camb. 43, 275.

    Google Scholar 

  • Glasstone, S. 1962.Textbook of Physical Chemistry. pp. 267. London: MacMillan.

    Google Scholar 

  • Ingram, M. 1969 InThe Bacterial Spore, G. W. Gould and A. Hurst (Eds). New York: Academic Press.

    Google Scholar 

  • Lea, D. E. 1955.Actions of Radiations on the Living Cell. Cambridge University Press.

  • Moats, W. A., R. Dabbah and V. M. Edwards. 1971.J. Food Sci. 36, 523.

    Google Scholar 

  • Pflug, I. J. and G. M. Smith. 1982. In Selected Papers on the Microbiology and Engineering of Sterilization, I. J. Pflug (Ed.), Minneapolis: Environmental Sterilization Lab.

    Google Scholar 

  • Rahn, D. 1945. InInjury and Death of Bacteria by Chemical Agents, p. 13. (Reprinted in Biodynamica Monograph No. 3. Luyet, B. J. (Ed.)).

  • Reif, F. 1965. Fundamentals of Statistical and Thermal Physics, p. 268. New York: McGraw-Hill.

    Google Scholar 

  • Stumbo, C. R. 1973. Thermobacteriology in Food Processing. New York: Academic Press.

    Google Scholar 

  • Vas, K. and G. Proszt. 1957.J. appl. Bact. 20 431.

    Google Scholar 

  • Withell, E. R. 1942.J. Hyg. 42, 124.

    Article  Google Scholar 

  • Wood, T. H. 1956.Adv. Biol. Med. Phys. 4, 119.

    Google Scholar 

  • Zimmer, K. G. 1961. In Studies on Quantitative Radiation Biology, Edinburgh. Oliver and Boyd.

    Google Scholar 

Download references

Author information

Author notes

  1. S. McKee

    Present address: University of Strathclyde, Glasgow

Authors and Affiliations

  1. Unilever Research, Colworth Laboratory, Colworth House, MK44 1LQ, Sharnbrook, Bedford, U.K.

    S. McKee & G. W. Gould (Professor of Industrial Mathematics)

Authors
  1. S. McKee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. W. Gould
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

McKee, S., Gould, G.W. A simple mathematical model of the thermal death of microorganisms. Bltn Mathcal Biology 50, 493–501 (1988). https://doi.org/10.1007/BF02458848

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458848

Keywords

Search

Navigation