Gompertz Function Approach: Numerical Integration for Microbial Growth Problem

In this work, we developed a numerical integrator using the Gompertz function model approach with the basic parameters as highlighted by Gompertz in finding and measure the growth in human cells as a basis function involving exponential, logarithmic, and polynomial, hence implemented the numerical integrator to solve problems arising in microbial growth staging. Microbial growth, synonymous to mildew or mold, which is a fungi family commonly found both indoors and outdoors. The indoors occur especially when there is humidity, moisture, oxygen, organic matters and low sunlight. Microbial growth which is the increase in the number of microbial cells which can also be in term of bacterial growth. It can be influenced by various factors to grow including temperature, Water, availability of oxygen, and other nutrient content. The growth staging can be in four phases such as lag, logarithmic, stationary and death phases. A culture of bacterial was taken, the approximate number of strand that was originally present and the growth were calculated using the numerical integration, the results obtained shows a significant, effective and robust improvement on the strand when compared the results with the exact solution. The properties of the integrator were analyzed, considering that Microbial Growth is an increase in the number of bacteria cells in a system when the proper nutrients and environment are provided. Therefore with the approach of Gompertz, the numerical integrator can be applied further to find the growth in each of the phases as they occurs.