Mathematical Modeling

Math 485/585
Modeling the growth of the population of the United States

• Modeling global population changes

  • We will use data provided by the U.S. Census Bureau. The folowing website contains a link to national population estimates between 1900 and 1999. Import this data into MATLAB. To do so, you may run the file census.m, which creates a matrix Np whose entries are the number of U.S. residents per year, between 1900 and 1999.
  • Plot the U.S. population as a function of time. What do you conclude?
  • Can the growth of the U.S. population be modeled by a simple evolution equation of the form N(t+1) = (1+R) N(t), where t is in years? Why or why not? If so, find R.
  • Post-census population estimates are obtained as described on the following methodology page. Read this information and explain the formula used to find estimates of the U.S. population.
  • Given the following estimates (from http://www.census.gov/popest/datasets.html), find the population of the U.S. in 2004:
    • Population in 2001: 285,102,075
    • Births, deaths, and net international immigration:
      • 2002: 4,006,985; 2,429,999; 1,262,159
      • 2003: 4,055,469; 2,432,874; 1,225,161
      • 2004: 4,099,399; 2,453,984; 1,221,013




• Model with different age groups

  • The following link contains population estimates by five-year age groups from 2000 to 2003.
    • Use this information to plot the age distribution in the U.S. for different years. You may import the following Excel file containing the same information.
    • Has there been major changes in the last 4 years?
    • The data has 21 age groups. Use the age distribution that you just plotted to define larger age groups that can be used in a simplified model.
  
  
  • Using birth and death rates for 2002, as published by the Center for Disease Control and Prevention, predict the population in the various age groups, taking the 2001 data as initial condition. You may look at Figures 3 and 2 in these documents, respectively. Note: do not attempt to print these files; they are more than 100 pages long!
  • How does your model compare to the estimates for 2003?
  • Use your model to predict the population in each age group in 2025. What do you conclude?