Tanzania Journal of Science 45(3): 346-354, 2019 ISSN 0856-1761, e-ISSN 2507-7961 © College of Natural and Applied Sciences, University of Dar es Salaam, 2019 Mathematical Model for Tanzania Population Growth Andongwisye J Mwakisisile1 and Allen R Mushi2* 1Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania. E-mail: [email protected] 2Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania. *Corresponding author, e-mail: [email protected] Abstract In this paper, a mathematical model for Tanzania population growth is presented. The model is developed by using exponential and logistic population growth models. Real data from censuses conducted by Tanzania National Bureau of Statistics (NBS) are used. The Tanzania growth rate is obtained by using data of 1967 and 2012 censuses. The prediction of population for the period of 2013 to 2035 is done. Numerical results show that the population grows at the rate of 2.88%. In 2035 the population is expected to be 87,538,767 by exponential model and 85,102,504 by logistic model. The carrying capacity is 2,976,857,550, which implies that the population will still grow faster since it is far from its limiting value. Comparisons of the models with real data from the five censuses are done. Also NBS projections are compared with populations predicted by the two models. Both comparisons show that the exponential model is performing better than logistic model. Also, the projection up to 2050 gives the population of 135,244,161 by exponential model and 131,261,794 by logistic model. Keywords: Population growth, Exponential model, Logistic model, Carrying Capacity. Introduction international development frameworks (NBS The size of a population is an important 2012). parameter for economic development. The Ofori et al. (2013) asserted that the major growth of population increases demands for issue of the World is tremendous growth of food, water, energy and other economic the population especially in developing needs. The growth of the population also countries in relation to services provision. determines the demand for essential social Population size and growth in a country can services, such as education, health, transport influence directly the situation of economy, and housing (NBS 2006). policy, culture, education and environment Knowing the future population is a core (Yahaya et al. 2017). factor for development planning and Many countries use census to get the decision making. Population projection actual number of their population. The provides future estimates of population size process is very costly; it involves a lot of needed by planners and policy makers. people and technologies. Consequently, Projections contribute to the improvement of based on the cost incurred, census cannot be quality of life of citizens through the conducted in short periods of time provision of current and reliable data for necessitating the use of projection models to policy formulation, development planning predict the future population. and service delivery as well as for Several mathematical population models monitoring and evaluating national and have been developed and applied. 346 http://journals.udsm.ac.tz/index.php/tjs www.ajol.info/index.php/tjs/ Tanz. J. Sci. Vol. 45(3), 2019 Mathematical models are very useful for when it is not known. They used a curve projecting the total population. That is, the fitting method for the population of a certain past data of the population is used to predict period of consecutive 11 years. The method the future population. The most popular and gave better predictions which were close to applied models are exponential and logistic. the actual values of population. The exponential growth model was Ofori et al. (2013) developed proposed by Malthus in 1798 and is also mathematical model for Ghana's population called the Malthusian growth model growth. They applied the exponential and (Malthus 1798). The model suggests that the logistic growth models to project the growth is exponential and has no bound. population. Their study found that the This model is widely regarded in the field of exponential model gave a better projection population ecology as the principle of compared to the logistic model. However, population dynamics ( Ashraf and Galor Ghana’s population properties are different 2008, Wali et al. 2012). from Tanzania, including growth rate, initial Logistic growth model was proposed by population and therefore carrying capacity Verhulst in 1845 (Marsden et al. 2003). The estimations. model is the extension of Malthusian model. Kulkarni et al. (2014) estimated the The main feature of logistic model is the population growth of India from 2009 to inclusion of the limiting value which is the 2012 using the logistic model approach and size of population that an environment can gave a comparison with actual population of support. This value is called carrying India for the same time period. An error capacity K. In this model, population equation was also deduced based on the increases faster when the number of people trend line for the specified time period and is very small compared to the value of the population of India for the year 2013 and carrying capacity (K) and slowly as the onwards till 2025 had been estimated. The population size is near to the value of time required for India to reach its carrying carrying capacity. capacity was also discussed. According to Matintu (2016), as the Wali et al. (2012) also studied the population increases, the environment ability application of logistic equation to model the to support population decreases and hence population growth of Uganda. They used the population reaches the stability point, least squares method to compute the growth that is, the carrying capacity. Therefore, it is rate, the carrying capacity and the year when reasonable to consider the mathematical the population of Uganda will approximately model which explicitly incorporates the idea be half of the carrying capacity. More works of carrying capacity. Both models originated in population modeling are found in Dawed from observations of biological reproduction et al. (2014), Shepherd and Stojkov (2005), processes (Wei et al. 2015). Most of the Law et al. (2003), Wali et al (2011) on successful models are based on the extended Rwanda) and many others. forms of these models. Few studies concerning Tanzania population have been conducted. For Literature Review example, Madulu (2004) discussed the Several studies have been conducted on linkages between population growth and mathematical population models. Ali et al. environmental degradation in Tanzania. (2015) studied census data and predicted Tanzania's major environmental problems, population of Bangladesh by using logistic demographic characteristics, and the model. They used a curve fitting method and linkages between environmental change and tried to compare the prediction between the rapid population growth both at national and case when carrying capacity is known and regional levels were discussed. A conclusion 347 Mwakisisile and Mushi - Mathematical model for Tanzania population growth made is that, environmental change is as an was in 1967 followed by the censuses of important factor to demographic and 1978, 1988, 2002 and 2012. These censuses economic factors as it is population growth contributed to the improvement of quality of to economic development and life through provision of current and reliable environmental conservation. data. The table below displays the In this paper, the mathematical model for population with respect to the year of the Tanzania population growth is studied. This census. model is adapted from the presented models in the literature but applies actual data from Table 1: Tanzania population from five NBS which is mostly used by the censuses Government for planning. This differs with Year Population most models in literature which use standard 1967 12,313,469 data from the International Data Base (IDB), United Nations and World Bank (Ogoke and 1978 17,512,610 Nduka 2016, Wali et al. 2012). The main 1988 23,174,335 objective of this work is to develop a 2002 34,443,603 population model by using mathematical 2012 44,928,923 modeling which is less costly and can be used for predicting future population. Table 1 shows that the population in 45 years has increased rapidly to more than 30 Tanzania population million people. Despite the high population, Tanzania is a relatively large country in the country is still sparsely populated, that East Africa. It shares boarders with Kenya, is, the density is high in some parts of the Uganda, Rwanda, Zambia, Malawi, country and has been increasing over time Mozambique, Burundi, Democratic (Madulu 2005). The Government of the Republic of Congo and also the Indian United Republic of Tanzania adopted the Ocean in the Eastern part. By area, Tanzania National Population Policy in 1992. The is the 31st largest country in the World and th policy encompasses the following items: 13 largest country in Africa (out of 54 population and development planning; countries of Africa) with the area of 947,303 equality, equity and social justice; square kilometres. Tanzania is estimated to reproductive health; natural resources; food be among the countries with highest birth production; information and databases, and rates in the World. According to DESA, UN th advocacy (URT 2006). (2017), by 2017 Tanzania was the 24 The policy provides a framework