Comparative Study of Mathematical Models for Population Growth in Ghana Prisons

Joseph Acquah, A. Buabeng, L. Brew


The study examined the population growth in the Ghana Prisons based on four growth models. The models examined were the Logistic, Gompertz, Gaussian and the Richards. All the models were then used to predict the population growth in the Ghana prisons up to 2025. Although all the approximated models gave a good estimation of the observed population growth of prisoners in Ghana, the Gompertz model was adjudged to give the best approximation. The model was selected based on its high proportion of variance as well as having the least value in terms of Root Mean Square Error (RMSE) and information loss. The model suggested that the population of prisoners in Ghana could increase to about 14 530 by 2025.


Sigmoid, Logistic, Gompertz, Gaussian, Richards, Prisoners, Population Growth

Full Text:



Aghababaie, M., Meheshti, M. and Khanahmadi, M. (2014), “Effect of Temperature on pH on forlulating the kinetic growth parameters and lactic production of Lactobacillus bulgaricus”, Biological Nutrition and Food Sciences Research, Vol. 1, pp. 49-56.

Akaike, H. (1973), “Information Theory and an Extension of the Maximum Likelihood Principle”, 2nd International Symposium on Information Theory, Budapest, pp. 267-281.

Anon. (2015), “Introduction to Project Efiase”, Accessed: June 10, 2018.

Anon. (2016), “Ghana's prisons overcrowded by 45.5%”, HomePage/NewsArchive/Ghana-s-prisons-overcrowded-by-45-5-450549. Accessed: June 6, 2018.

Appiah, S. T., Wiah, E. N., Brew, L. and Kwateng, F, (2016), “Comparative Study of Mathematical Models for Population Projection”, 2nd UMaT Biennial International Mining and Mineral Conference, Tarkwa, pp. 359-365.

Bimpeh, J. K. (2017), Crime rate reduced by 10% between January and May 2017, Prime News Ghana, general-news/igp-refutes-assertions-of-crime-ascendency-in-the-country.html. Accessed: June 18, 2018.

Burnham, K. P., Anderson, D. R. and Huyvaert, K. P. (2011), “AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons”, Behavioral Ecology and Sociobiology, Vol. 65, No. 1, pp. 23-35.

Catlin, D. H., Felio, J. H. and Fraser, J. D. (2013), “Effects of water discharge on fledging time, growth, and survival on piping plovers on the Missouri river”, Management and Conservation, Vol. 77, No. 3, pp. 525-533.

Cavanaugh, J. E. (1997), “Unifying the derivations of the Akaike and corrected Akaike information criteria”, Statistics & Probability Letters, Vol. 31: 201–208.

Gompertz, B. (1825), “On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies”, Philos. Trans. Roy. Soc., Vol. 123, pp. 513-585.

Guo, H. (2011), A Simple Algorithm for Fitting a Gaussian Function, IEEE, Vol. 28, No. 5, pp. 134-137.

Hagen, N., Kupinski, M. and Dereniak, E. L. (2007), “Gaussian profile estimation in one dimension”, Appl. Opt., Vol. 46, pp. 5374-5383.

Müller, J. And Dirner, V. (2010), “Using Sigmoid Functions for Modelling South African Gold Production”, GeoScience Engineering, Vol. LVI, No. 2, pp. 44-58.

Nutsupkui, (2011), “Ghana Prisons Service Ten-Year Strategic Development Plan”, Accessed: June 2, 2018.

Tjørve, K. C. M, and Tjørve, E. (2017), “Modelling avian growth with the Unified-Richards: As exemplifed by wader-chick growth”, Journal of Avian Biology, Vol. 48, No. 6, pp. 770-778.

Verhulst, P. F. (1838), “Notice sur la loi que la population suit dans son accroissement”, Corr. Math. Physics, Vol. 10, pp. 113-121.


  • There are currently no refbacks.