Mathematical Modeling Of The Carrying Capacity Of The Population In Beijing And Shanghai

Carrying capacity is one of the important tools on organizing development of population,resources,and environment.It can be defined as the maximum plenty of the population that an environment can maintain under limited resources and it is also deemed the limiting factor of population or an ecosystem.In this thesis,we propose a mathematical model that describes the population and use it to simulate the real data of Beijing and Shanghai cities,P.R China from 1980-2016.The logistic equation was used in this study because it is more useful and widely used for examining population growth.The carrying capacity of Beijing and Shanghai population is estimated using simulation method.Our results show that the maximum carrying capacity of population size in Beijing and Shanghai are 2 7-56 million and 2 729 million,respectively.However,the population sizes in both cities are approaching to the maximum carrying capacity.The optimal control strategy is the best method for decreases the population size of both cities by establishing sub-cities for example Xiongan Xinqu of Beijing.This thesis contains four chapters.The first chapter consists of five sections.In section one,we presented an introduction about the fundamental concepts and definitions of carrying capacity and the importance of mathematical models in analyzing and solving real problems.The literature review of carrying capacity is introduced in section two.Section three and section four contains the background of Malthusian growth model and Logistic growth model respectively.Overview of the Chi-Square test and its types are introduced in section five.In second chapter,we used our model to simulate the real data of Beijing population from 1980 to 2016 using Matlab software to find the optimal values of parameters:the carrying capacity of the population(K)and the intrinsic growth rate(r)and calculate the confidence interval of carrying capacity.We used the ode45 to solve the model in this numerical simulation.In third chapter,we used our model to simulate the real data of Shanghai population from 1980 to 2016 using Matlab software to find the optimal values of K and r and calculate the confidence interval of carrying capacity.The ode45 was used to solve the model in this numerical simulation.The brief discussion and conclusion are presented in chapter four.