Gompertz Function Approach: Numerical Integration for Microbial Growth Problem

Ayinde Samuel Olukayode; Omowaye Adeola John; Fadugba Sunday Emmanuel; Adebayo Kayode James; Ogunmiloro Oluwatayo Micheal; Olarinde Oluwakemi Oluwaseun

doi:doi:10.11648/j.acm.20251402.12

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Gompertz Function Approach: Numerical Integration for Microbial Growth Problem

Ayinde Samuel Olukayode^*

, Omowaye Adeola John

, Fadugba Sunday Emmanuel

, Adebayo Kayode James

, Ogunmiloro Oluwatayo Micheal

, Olarinde Oluwakemi Oluwaseun

Published in Applied and Computational Mathematics (Volume 14, Issue 2)

Received: 28 February 2025 Accepted: 11 March 2025 Published: 28 March 2025

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Abstract

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.

Published in	Applied and Computational Mathematics (Volume 14, Issue 2)
DOI	10.11648/j.acm.20251402.12
Page(s)	90-100
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Numerical Integrator, Gompertz Function, Microbial Growth and Bacteria Cells

References

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[2]	Fatunla S. O. (1988), Numerical Method for initial value problems of ODEs. Academic Press, San Diego, USA.
[3]	Gear, W., (1971). Numerical initial value problems in ODEs, Prentice Hall, Englewood Cliffs, NJ.
[4]	Gompertz B. (1860). On one uniform Law of Mortality from Birth to Extreme old age and on the law of sickness. Presented to internal Statistical congress in 1860 and reported in 1871. Journal of the Institute of Actuaries. 16, 329-344. https//www.jstor.org/stable/41135309
[5]	Henrici, P. (1962). Discrete Variable Methods in ODEs. New York, John Wiley and Sons, USA.
[6]	Lambert, J. D. (1962). Numerical Methods for Ordinary Differential Systems. Wiley. New York.
[7]	Linda D. B. (2021). Microbial Growth. Biology Libre Texts. Bio.Libretexts.org Oregon State University, USA.
[8]	Mehrara E., Forsell A. E., Johanson V., Koolby L., Hultborn R., Bernhardt P. (2013). “A new method to estimate parameters of the growth model for metastatic Tumors.” Theoretical Biology Medical Model. 10: 31-43. https://doi.org/10.1186/1742-4682-10-31
[9]	Ogunrinde R. B. and Ayinde S. O. (2017). A Numerical Integration for solving first order differential equation using Gompertz Function Approach. American Journal Computational and Applied Mathematics. 7(6): 143-148. https://doi.org/10.5923/j.ajcam.20170706.01
[10]	Uruburu, F. (2003). History and Services of Culture Collections. International Microbiology. 6(2): 101-103. https://doi.org/10.1007/s10123-003-0115-2
[11]	Sergio, R., Annie, D., and Hubert, M. (2003). “Application of the Gompertz Equation for the study of Xylem Cell Development”. Dendrochronologia. Urban and Fisher Verlag. 21/1: 1-7. ISSN: 1125-7865.
[12]	Stoer, J. and Bulirsh, R., (1966). “Numerical Treatment of ODEs by Extrapolation Methods” Numerische Mathematical. 8, 93-104.
[13]	Winsor, C. P. (1932). “The Gompertz Curve as a Growth Curve”. Proceedings of the National Academy of Sciences. USA. Vol 18, No1, 1-8.
[14]	Zuhaimy, I., Acme, K. and Md-Yunus, J. (2003). “fitting Nonlinear Gompertz curve to Tobacco Growth Data”. Pakistan Journal of Agronomy. 2(4); 223-236. ISSN: 1680-8207.
[15]	Zwietering, M. H. (1990), "Modeling of the Bacterial Growth Curve", Applied and Environmental Microbiology 56 (6): 1875-1881. https://www.dreamstime.com/stock-photography-fish-feeding-image © 2003-2018.

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APA Style

Olukayode, A. S., John, O. A., Emmanuel, F. S., James, A. K., Micheal, O. O., et al. (2025). Gompertz Function Approach: Numerical Integration for Microbial Growth Problem. Applied and Computational Mathematics, 14(2), 90-100. https://doi.org/10.11648/j.acm.20251402.12

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ACS Style

Olukayode, A. S.; John, O. A.; Emmanuel, F. S.; James, A. K.; Micheal, O. O., et al. Gompertz Function Approach: Numerical Integration for Microbial Growth Problem. Appl. Comput. Math. 2025, 14(2), 90-100. doi: 10.11648/j.acm.20251402.12

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AMA Style

Olukayode AS, John OA, Emmanuel FS, James AK, Micheal OO, et al. Gompertz Function Approach: Numerical Integration for Microbial Growth Problem. Appl Comput Math. 2025;14(2):90-100. doi: 10.11648/j.acm.20251402.12

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@article{10.11648/j.acm.20251402.12,
  author = {Ayinde Samuel Olukayode and Omowaye Adeola John and Fadugba Sunday Emmanuel and Adebayo Kayode James and Ogunmiloro Oluwatayo Micheal and Olarinde Oluwakemi Oluwaseun},
  title = {Gompertz Function Approach: Numerical Integration for Microbial Growth Problem},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {2},
  pages = {90-100},
  doi = {10.11648/j.acm.20251402.12},
  url = {https://doi.org/10.11648/j.acm.20251402.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251402.12},
  abstract = {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.},
 year = {2025}
}

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TY  - JOUR
T1  - Gompertz Function Approach: Numerical Integration for Microbial Growth Problem
AU  - Ayinde Samuel Olukayode
AU  - Omowaye Adeola John
AU  - Fadugba Sunday Emmanuel
AU  - Adebayo Kayode James
AU  - Ogunmiloro Oluwatayo Micheal
AU  - Olarinde Oluwakemi Oluwaseun
Y1  - 2025/03/28
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251402.12
DO  - 10.11648/j.acm.20251402.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 90
EP  - 100
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20251402.12
AB  - 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.
VL  - 14
IS  - 2
ER  -

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Author Information

Ayinde Samuel Olukayode

Mathematics Department, Ekiti State University, Ado Ekiti, Nigeria

Contact Email

http://orcid.org/0000-0002-1742-7161
Omowaye Adeola John

Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria

Contact Email

http://orcid.org/0000-0003-0492-8271
Fadugba Sunday Emmanuel

Mathematics Department, Ekiti State University, Ado Ekiti, Nigeria

Contact Email

http://orcid.org/0000-0003-0911-6838
Adebayo Kayode James

Mathematics Department, Ekiti State University, Ado Ekiti, Nigeria

Contact Email

http://orcid.org/0000-0003-3684-6190
Ogunmiloro Oluwatayo Micheal

Mathematics Department, Ekiti State University, Ado Ekiti, Nigeria

Contact Email

http://orcid.org/0000-0002-0800-3690
Olarinde Oluwakemi Oluwaseun

Mathematics Department, Ekiti State University, Ado Ekiti, Nigeria

Contact Email

http://orcid.org/0009-0001-7536-6299

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Plain Text BibTeX RIS

APA Style

Olukayode, A. S., John, O. A., Emmanuel, F. S., James, A. K., Micheal, O. O., et al. (2025). Gompertz Function Approach: Numerical Integration for Microbial Growth Problem. Applied and Computational Mathematics, 14(2), 90-100. https://doi.org/10.11648/j.acm.20251402.12

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ACS Style

Olukayode, A. S.; John, O. A.; Emmanuel, F. S.; James, A. K.; Micheal, O. O., et al. Gompertz Function Approach: Numerical Integration for Microbial Growth Problem. Appl. Comput. Math. 2025, 14(2), 90-100. doi: 10.11648/j.acm.20251402.12

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AMA Style

Olukayode AS, John OA, Emmanuel FS, James AK, Micheal OO, et al. Gompertz Function Approach: Numerical Integration for Microbial Growth Problem. Appl Comput Math. 2025;14(2):90-100. doi: 10.11648/j.acm.20251402.12

Copy | Download

@article{10.11648/j.acm.20251402.12,
  author = {Ayinde Samuel Olukayode and Omowaye Adeola John and Fadugba Sunday Emmanuel and Adebayo Kayode James and Ogunmiloro Oluwatayo Micheal and Olarinde Oluwakemi Oluwaseun},
  title = {Gompertz Function Approach: Numerical Integration for Microbial Growth Problem},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {2},
  pages = {90-100},
  doi = {10.11648/j.acm.20251402.12},
  url = {https://doi.org/10.11648/j.acm.20251402.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251402.12},
  abstract = {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.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Gompertz Function Approach: Numerical Integration for Microbial Growth Problem
AU  - Ayinde Samuel Olukayode
AU  - Omowaye Adeola John
AU  - Fadugba Sunday Emmanuel
AU  - Adebayo Kayode James
AU  - Ogunmiloro Oluwatayo Micheal
AU  - Olarinde Oluwakemi Oluwaseun
Y1  - 2025/03/28
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251402.12
DO  - 10.11648/j.acm.20251402.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 90
EP  - 100
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20251402.12
AB  - 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.
VL  - 14
IS  - 2
ER  -

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