The conformability of two equations for bacterial growth in pork

Abstract

Pork is now distributed as cut meat, which increases the chance of contamination with bacteria. The rate of bacterial growth can be expressed by an exponential function. In order to find how the number of contaminating bacteria increases, we compared two functional equations for a growth curve. They are logistic: Yt = K (1 + m e-at) (1) and Gompertz: log Yt = log K + (log a)bt (2) equations (where Yt = the number of bacteria at the time t in min, m and a = coefficient, e = natural logarithm, K maximum number of bacteria). 90 ml of physiological salt solution was added to 10 g of pork. It was homogenized for 3 min, then incubated at 35°C for 13 hrs. The number of bacteria was counted every hour. We found from these data that the above two equations can be expressed as follows: Yt = 23 535 (1 + 16269 e-1.1608t) and log Yt = 8.9940 + (-3.1124) × 0.7839t. The theoretical and actual values matched well in equation (1), and the number of bacteria can be predicted accurately using this equation at a given time after incubation. The theoretical and actual values did not match well in equation (2) and its accuracy to predict the number of bacteria was very low except the initial number of bacteria was high.

Keywords

• logistic equation
• mathematical model
• micro-organismus
• gompertz