Applied and Computational Mathematics 2014; 3(4): 171-176 Published online August 30, 2014 (http://www.sciencepublishinggroup.com/j/acm) doi: 10.11648/j.acm.20140304.18 ISSN: 2328-5605 (Print); ISSN: 2328-5613 (Online) Mathematical model for the population dynamics of the Serengeti ecosystem Janeth James Ngana 1 , Livingstone Serwadda Luboobi 2 , Dmitry Kuznetsov 1 1 Nelson Mandela African Institution of Science and Technology (NM-AIST), Arusha, Tanzania 2 Department of Mathematics, Makerere University, Kampala, Uganda Email address: nganaj@nm-aist.ac.tz (J. J. Ngana), luboobi@cns.mak.ac.ug (L. S. Luboobi), dmitry.kuznetsov@nm-aist.ac.tz (D. Kuznetsov) To cite this article: Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov. Mathematical Model for the Population Dynamics of the Serengeti Ecosystem. Applied and Computational Mathematics. Vol. 3, No. 4, 2014, pp. 171-176. doi: 10.11648/j.acm.20140304.18 Abstract: Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased. Keywords: Carnivores, Herbivores, Grass, Population Dynamics, Migration, Ecosystem, Wildebeest 1. Introduction There is nowhere else in the world where there is such a movement of animals as immense as the wildebeests (Connochaetes taurinus), zebras (Equus burchelli) and Thomson’s gazelle (Gazella thomsoni), migrating from Serengeti National Park in Tanzania to Masai Mara National Reserve in Kenya and back. The wildebeest (Connochaetes taurinus) migration in the Serengeti/ Mara ecosystem of Tanzania and Kenya represents an iconic example of ungulate migration and constitutes one of the most thoroughly documented animal migrations in one of the most intensively studied ecosystems on earth [13, 8, 2, 9, 16, 17, 15, 10]. The migration is driven by a marked, highly seasonal rainfall gradient, increasing from South East to North West, coupled with strong differences in soil fertility and plant nutritional content between the grassland and savanna habitats [8, 6, 5, 11]. Speaking of population trends and predation, by using a logistic model equation for estimating the wildebeest’s population, from 1960s to 1980s, the Serengeti-Mara ecosystem witnessed dramatic changes. By mid-1970s, the wildebeest population increased by a factor of five, and remained at approximately 1.3 million with slight variations [14, 3, 12]. Reconstruction of 100 years of the vegetation dynamics in the Serengeti ecosystem gives an insight of what might happen if the wildebeest population is reduced to about 200,000, as it is believed to have been following the Rinderpest epidemic in the early 1900s [4]. The Thomson’s gazelles population has been declining almost two thirds over a decade ago. This decline has been due to: predation, interspecific competition and diseases. Predation has been found to be the main factor preventing the increase of the Thomson’s gazelles population at the Serengeti National Park [1]. Imposing seasonal variation to multispecies models that in a constant environment tend towards a stable equilibrium can lead to cycles and even chaotic dynamics [7], with overcompensating density dependence leading to low population densities where extinction may be risked. In this paper we formulate and analyze a population dynamics model that depicts the food chain relationship between: grass; herbivores (wildebeest, zebra and Thomson’s gazelles); carnivore predators (lions and crocodiles); thus reflecting on grass food factor, the