Akgakaya HR, Ginzburg LR, Slice D, and Slobodkin LB (1988) The theory of population dynamics - II. Physiological delays. Bulletin of Mathematical Biology 50(5): 503-515.
Alee WC (1931) Animal Aggregations - A Study in General Sociology. Chicago: University of Chicago Press.
Augustin JC and Carlier V (2000) Mathematical modelling of the growth rate and lag time for Listeria monocytogenes. International Journal of Food Microbiology 56: 29-51.
Baranyi J (2002) Stochastic modelling of bacterial lag phase. International Journal of Food Microbiology 73: 203-206.
Baranyi J and Roberts TA (1994) A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23: 277-294.
Baranyi J, Roberts TA, and McClure PJ (1993) A non-autonomous differential equation to model bacterial growth. Food Microbiology 10: 43-59.
Baty F and Delignette-Muller ML (2004) Estimating the bacterial lag time: Which model, which precision? International Journal of Food Microbiology 91: 261-277.
Buchanan RL, Whiting RC, and Damert WC (1997) When is simple good enough: A comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves. Food Microbiology 14: 313-326.
Carlson T (1913) Uber Geschwindigkeit and Grosse der
Hefevermerbrung in würze. Biochemische Zeitschirft 57: 313-334.
Farber JM, Cai Y, and Ross WH (1996) Predictive modeling of the growth of Listeria monocytogenes in CO2 environments. International Journal of Food Microbiology 32: 133-144.
Galilei G (1632) Dialogo Sopra i Due Massimi Sistemi Del Mondo (Dialogue Concerning the Two Chief World Systems) Florence.
Gibson AM, Bratchell N, and Roberts TA (1988) Predicting microbial growth: Growth responses of salmonellae in a laboratory medium as affected by pH, sodium chloride and storage temperature. International Journal of Food Microbiology 6: 155-178.
Ginzburg LR (1986) The theory of population dynamics: I. Back to first principles. Journal of Theoretical Biology 122: 385-399.
Gompertz B (1825) On the nature of the function expressive of the law of human mortality, and a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115: 513-583.
Hills BP and Wright KM (1995) Multi-compartment kinetic models for injury, resuscitation, induced lag and growth in bacterial cell populations. Food Microbiology 12: 333-346.
Hutchinson GE (1948) Circular casual systems in ecology. Annals of the New York Academy of Sciences 50: 211-246.
Maier RM (1999) Bacterial growth. In: Maier RM, Pepper IL, and Gebra CP (eds.) Environmental Microbiology, 44pp. San Diego: Academic publisher.
Malthus TR (1798) An Essay on the Principle of Population. Harmondsworth: Penguin.
May M Robert and Sir (1973) Time-delay versus stability in population models with two and three trophic levels. Ecology 54: 315-325.
May M Robert and Sir (1978) Mathematical aspects of the dynamics of animal populations. In: In: Levin SA (ed.) Studies in Mathematical Biology - Part II: Populations and Communities, Studies in Mathematics, vol. 16, pp. 317-366. Washington, DC: The Mathematical Association of America.
May M Robert and Sir (1981) Models for single populations. In: May RM (ed.) Theoretical Ecology, pp. 5-29. Oxford: Blackwell Scientific Publications.
McClure PJ, Baranyi J, Boogard E, Kelly TM, and Roberts TA (1993) A predictive model for the combined effect of pH, sodium chloride and storage temperature on the growth of Brochothrix thermosphacta. International Journal of Food Microbiology 19: 161-178.
McClure PJ, Cole MB, and Davies KW (1994) An example of the stages in the development of a predictive mathematical model for microbial growth: The effects of NaCl, pH and temperature on the growth of Aeromonas hydrophila. International Journal of Food Microbiology 23: 359-375.
McKellar R and Lu X (2003) Modeling Microbial Responses in Foods. Boca Raton: CRC Press, (ISBN 0-8493-1237-X).
McMeekin TA, Olley J, Ratkowsky DA, and Ross T (2002) Predictive microbiology: Towards the interface and beyond. International Journal of Food Microbiology 73: 395-407.
McMeekin TA and Ross T (2002) Predictive microbiology: Providing a knowledge-based framework for change management. International Journal of Food Microbiology 23: 359-375.
Messen W, Verluyten J, Leroy F, and De Vuyst L (2002) Modelling growth and bacteriocin production by Lactobacillus curvatus LTH 1174 in response to temperature and pH values used for European sausage fermentation processes. International Journal of Food Microbiology 81: 41-52.
Meyer PS (1994) Bi-logistic growth. Technological Forecasting and Social Change 47: 89-102.
Meyer PS and Ausubel JH (1999) Carrying capacity: A model with logistically varying limits, Technological Forecasting and Social Change 47: 89-102.
Monod J (1942) Recherches Sur la Croissance des Cultures Bacteriennes. Paris: Herman.
Murray BG (1992) Research methods in physics and biology. Oikos 64: 594-596.
Newton Issac, Sir (1687) Philosophiae Naturalis Principia Mathematica.
O'Donovan L and Brooker JD (2001) Effect of hydrolysable and condensed tannins on growth, morphology and metabolism of Streptococcus gallolyticus (S. caprinus) and Streptococcus bovis. Microbiology 147: 1025-1033.
Pearl R (1927) The growth of populations. The Quarterly Review of Biology II(4): 532-548.
Pirt SJ (1975) Growth lag. In: Principles of Microbe and Cell Cultivation. London: Blackwell.
Richards FJ (1959) A flexible growth function for empirical use. Journal of Experimental Botany 10: 290-300.
Smith FE (1963) Population dynamics in Daphnia magma. Ecology 44: 651-663.
Swinnen IAM, Bernaerts K, Dens EJJ, Geeraerd AH, and Van Impe JF (2004) Predictive modeling of the microbial lag phase: A review. International Journal of Food Microbiology 94: 137-159.
Tsoularis A and Wallace J (2002) Analysis of logistic growth models. Mathematical Biosciences 179: 21-55.
Turchin P (2001) Does population ecology have general laws? Oikos 94: 17-26.
Turner ME, Jr., Bradley EL, Jr., and Kirk KA (1976) A theory of growth. Mathematical Biosciences 29: 367-373.
Vadasz P and Vadasz AS (2002) The neoclassical theory of population dynamics in spatially homogeneous environments - Part I: Derivation of universal laws and monotonic growth. Physica A 309(3-4): 329-359.
Vadasz P and Vadasz AS (2002) The neoclassical theory of population dynamics in spatially homogeneous environments - Part II: Nonmonotonic dynamics, overshooting and oscillations. Physica A 309(3-4): 360-380.
Vadasz P and Vadasz AS (2006) Biological implications from an autonomous version of Baranyi & Roberts growth model. International Journal of Food Microbiology 114: 357-365.
Vadasz P and Vadasz AS (2005) Predictive modeling of microorganisms: LAG and LIP in monotonic growth. International Journal of Food Microbiology 102: 257-275.
Vadasz AS, Vadasz P, Abashar ME, and Gupthar AS (2001) Recovery of an oscillatory mode of batch yeast growth in water for a pure culture. International Journal of Food Microbiology 71(2-3): 219-234.
Vadasz AS, Vadasz P, Abashar ME, and Gupthar AS (2002) Theoretical and experimental recovery of oscillations during batch growth of a mixed culture of yeast in water. World Journal of Microbiology & Biotechnology 18(3): 239-246.
Vadasz AS, Vadasz P, Gupthar AS, and Abashar ME (2002) Theoretical and experimental recovery of oscillations during batch yeast growth in a pure culture subject to nutritional stress. Journal of Mechanics in Medicine and Biology 2(2): 147-163.
Verhulst PF (1838) Notice sur la loi que la population suit dans son accroissement. Correspondence Mathématique et Physique Publiee par A. Quetelet Tome X: 113-121.
von Bertalanffy L (1957) Quantitative laws in metabolism and growth. Quarterly Review of Biology 32: 217.
WangerskyPJ and Cunningham WJ (1957) Time lag in population models. Cold Spring Harbor Symposia on Quantitative Biology 22: 329-338.
Zwietering MH, Jongenburger I, Rombouts FM, and van't Riet K (1990) Modeling of the bacterial growth curve. Applied Environmental Microbiology 56: 1875-1881.
Was this article helpful?
Learning About 10 Ways Fight Off Cancer Can Have Amazing Benefits For Your Life The Best Tips On How To Keep This Killer At Bay Discovering that you or a loved one has cancer can be utterly terrifying. All the same, once you comprehend the causes of cancer and learn how to reverse those causes, you or your loved one may have more than a fighting chance of beating out cancer.