Mathematical modeling of Rwanda’s population growth

Abstract

Rwanda is a small landlocked African country located in Central Africa. It borders Democratic Republic of Congo, Uganda, Tanzania and Burundi. It has a total area of 26,338 square kilometers comprising 24,668 square kilometers of land and 1,670 square kilometers of water. Most of the country is savanna grassland with the population predominantly rural. It is a country characterized with a high population density. This paper centers on the application of the logistic growth model to model the population growth of Rwanda using data from the years 1980 to 2008 (inclusive). We have determined the carrying capacity and the vital coefficients governing the population growth of Rwanda. The results from the predictions show that the carrying capacity for the population of Rwanda is 77208025.64 and that the vital coefficients a and b are 0.03 and 3.88566419×10−10 , respectively. Thus the population growth rate of Rwanda, according to this model, is 3% per annum. This approximated population growth rate compares well with statistically predicted values in literature. Based on this modelwe also predict that the population of Rwanda will be 38604012.82 in the year 2067. The data used were collected from National Institute of Statistics of Rwanda (NISR) and International Data Base (IDB). It was analyzed using MATLAB and Statistical Package for Social Science (SPSS) and it accurately fitted the logistic growth curve.